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THE  PLANET  JUPITER 
As  seen  with  the  26  inch  telescope  at  "Washington,  1875,  June  24. 


AMERICAN  SCIENCE  SERIES,  BRIEFER  COURSE. 


ASTEONOMT 


SIMON    NEWCOMB,   LL.D. 

SUPERINTENDENT  AMERICAN    EPHSMERI3    AND  NAUTICAL  ALMANAC 
AND 

EDWARD    S.    HOLDEN,   M.A. 

DIRECTOR    OF  THE    WA8HBURN    OBSERVATORY 


SECO 


ox,  REVISED  AKD  ENLARGED. 


1STEW  YORK 
HENRY  HOLT  AND   COMPANY 

1885 


Copyright,  1883 

BY 

HENRY  HOLT  &  Co. 


PBEFACE. 


THE  present  treatise  is  a  condensed  edition  of  the  Astronomy  of 
the  American  Science  Series.  The  book  has  not  been  shortened  by 
leaving  out  anything  that  was  essential,  but  by  omitting  some  of  the 
details  of  practical  astronomy,  thus  giving  to  the  descriptive  por- 
tions a  greater  relative  extension. 

The  most  marked  feature  of  this  condensation  is,  perhaps,  the 
omission  of  most  of  the  mathematical  formulae  of  the  larger  treatise. 
The  present  work  requires  for  its  understanding  only  a  fair  acquaint- 
ance with  the  principles  of  algebra  and  geometry  and  a  slight 
knowledge  of  elementary  physics.  The  space  which  has  beeo  gained 
by  these  omissions  has  been  utilized  in  giving  a  fuller  discussion  of 
the  more  elementary  parts  of  the  subject,  and  in  treating  the  funda- 
mental principles  from  various  points  of  view. 

A  familiar  and  secure  knowledge  of  these  is  essential  to  the 
students'  real  progress.  The  full  index  makes  the  work  of  value  as 
a  reference-book  to  a  student  who  has  studied  it  and  put  it  aside. 

As  in  the  larger  work,  the  matter  is  given  in  two  sizes  of  type.  It 
will  be  found  that  the  larger  type  contains  a  course  practically  com- 
plete in  itself,  and  that  the  matter  of  the  smaller  type  is  chiefly  ex- 
planatory of  the  former.  It  is  highly  desirable,  however,  that  the 
book  should  be  read  as  a  whole,  while  the  actual  class -work  may  be 
confined  to  the  subjects  treated  in  the  larger  type,  if  the  class  is 
pressed  for  time.  A  celestial  globe,  and  a  set  of  star-maps  (PROC- 
TOR'S "  New  Star- Atlas"  is  as  good  as  any),  will  be  found  to  be  of 
use  in  connection  with  the  study ;  and  if  the  class  has  access  to  a  small 
telescope,  even,  much  can  be  learned  in  this  way.  A  mere  opera- 
glass  will  suffice  to  give  a  correct  notion  of  the  general  features  of 
the  moon's  surface,  and  a  very  small  telescope,  if  properly  used,  will 
do  the  same  for  the  larger  planets. 


CONTENTS. 


PAET  I. 

INTRODUCTION. 

PAGE 

Astronomy  Defined — How  to  Study  Astronomy — Angles:  their 
Measure — Plane  Triangles — The  Sphere — Power  of  the  Eye 
to  See  Small  Objects — Latitude  and  Longitude — Symbols 
and  Abbreviations 1 

CHAPTER  I. 
RELATION  OF  THE  EARTH  TO  THE  HEAVENS. 

The  Earth's  Shape  and  Dimensions — The  Celestial  Sphere — The 
Horizon — The  Diurnal  Motion — Diurnal  Motion  in  Different 
Latitudes — Correspondence  of  the  Terrestrial  and  Celestial 
Spheres 13 

CHAPTER  II. 
RELATION  OP  THE  EARTH  TO  THE  HEAVENS — (Continued). 

The  Celestial  Sphere — Systems  of  Coordinates — Relation  of  Time 
to  the  Sphere — Sidereal  Time — Solar  Time— Determinations 
of  Terrestrial  Longitudes — Where  does  the  Day  Change  ? 
— Determination  of  Latitudes— Parallax 37 

CHAPTER  III. 
ASTRONOMICAL  INSTRUMENTS. 

The  Telescope — Chronometers  and  Clocks — The  Transit  Instru- 
ment—The Meridian  Circle— The  Equatorial— The  Sextant 
—The  Nautical  Almanac. .....,,,. .,,,,,.,,.,,,,  60 


vi  CONTENTS. 

CHAPTER  IV. 
MOTIONS  OF  THE  EARTH. 

FAGK 

Ancient  Ideas  of  the  Planets— Annual  Revolution  of  the  Earth 
—The  Sun's  Apparent  Path— Obliquity  of  the  Ecliptic— 
The  Seasons — Celestial  Latitude  and  Longitude 81 

CHAPTER  V. 
THE  PLANETARY  MOTIONS. 

Apparent  and  Real  Motions  of  the  Planets  —  The  Copernican 
System  of  the  World — Kepler's  Laws  of  Planetary  Motion . .  96 

CHAPTER  VI. 
UNIVERSAL  GRAVITATION. 

Newton's  Laws  of  Motion — Gravitation  in  the  Heavens — Mutual 
Action  of  the  Planets— Remarks  on  the  Theory  of  Gravi- 
tation   113 

CHAPTER  VII. 
THE  MOTIONS  AND  ATTRACTION  OF  THE  MOON. 

The  Moon's  Motions  and  Phases— The  Tides— Effect  of  the 
Tides  upon  the  Earth's  Rotation 123 

CHAPTER  VIII. 
ECLIPSES  OF  THE  SUN  AND  MOON. 

The  Earth's  Shadow — Eclipses  of  the  Moon— Eclipses  of  the 
Sun — The  Recurrence  of  Eclipses 129 

CHAPTER  IX. 
THE  EARTH. 

Mass  and  Density  of  the  Earth — Laws  of  Terrestrial  Gravitation — 
Figure  and  Magnitude  of  the  Earth — Geodetic  Surveys — 
Motions  of  the  Earth's  Axis,  or  Precession  of  the  Equinoxes 
— Sidereal  and  Equinoctial  Year— The  Causes  of  Precession  142 


CONTENTS.  Vii 

CHAPTER  X. 

CELESTIAL  MEASUREMENTS  OF  MASS  AND  DISTANCE. 

PAGE 

The  Celestial  Scale  of  Measurement — Measures  of  the  Solar  and 
Lunar  Parallax — Methods  of  Determining  the  Solar  Parallax 
—Relative  Masses  of  the  Sun  and  Planets '. 158 

CHAPTER  XI. 
THE  REFRACTION  AND  ABERRATION  OF  LIGHT  ;  TWILIGHT. 

Atmospheric  Refraction — Quantity  and  Effects  of  Refraction — 
Twilight — Aberration  and  the  Motion  of  Light — Discovery 
and  Effects  of  Aberration 169 

CHAPTER  XII. 

CHRONOLOGY. 

Astronomical  Measures  of  Time — Formation  of  Calendars — 
Kinds  of  Months  and  Years,  Old  and  New  Style — Divi- 
sions of  the  Day — Equation  of  Time 180 


PAET  II. 

THE  SOLAR  SYSTEM  IN  DETAIL. 

CHAPTER  I. 
STRUCTURE  OF  THE  SOLAR  SYSTEM. 

Planets— Asteroids — Comets — Planetary  Aspects — Tables  of  the 
Elements  of  the  Solar  System 190 

CHAPTER  II. 

THE  SUN. 

General  Summary — The  Photosphere — Light  and  Heat  from 
the  Photosphere — Amount  of  Heat  Emitted  by  the  Sun — 
Solar  Temperature — Sun-Spots  and  Faculse — Solar  Axis 
and  Equator — Nature  of  Sun-Spots — Number  and  Periodic- 
ity of  Solar  Spots — The  Sun's  Chromosphere  and  Corona 
— Gaseous  Nature  of  the  Prominences — The  Coronal  Spec- 
trum— Sources  of  the  Sun's  Heat — Theories  of  the  Sun's 
Constitution..  ....  200 


Vlii  CONTENTS. 

CHAPTER  IIL 

THE  INFERIOR  PLANETS. 

PAGE 

Motions  and  Aspects — Atmosphere  and  Rotation  of  Mercury — 
Atmosphere  and  Rotatiou  of  Veu us— Transits  of  Mercury 
and  Venus — Supposed  Intramercurial  Planets 221 

CHAPTER  IV. 
THE  MOON. 

Character  of  the  Moon's  Surface — Lunar  Atmosphere — Light 
and  Heat  of  the  Moon— Is  there  any  Change  on  the  Surface 
of  the  Moot? 228 

CHAPTER  V. 
THE  PLANET  MARS. 

Description  of  the  Planet  —  Rotation  —  Surface  —  Satellites  of 
Mars 233 

CHAPTER  VI. 

THE  MINOR  PLANETS 

The  Number  of  Small  Planets— Their  Magnitudes— Forms  of 

their  Orbits— Origin 237 

» 

CHAPTER  VII. 

JUPITER  AND  ins  SATELLITES. 

The  Planet  Jupiter— Satellites  of  Jupiter 240 

CHAPTER  VIIL 

SATURN  AND  HIS  SYSTEM. 
General  Description— The  Rings  of  Saturn— Satellites  of  Saturn  246 

CHAPTER  IX. 

THE  PLANET  URANUS. 

Discovery — Satellites .  353 


CONTENTS.  ix 

CHAPTER  X. 

THE  PLANET  NEPTUNE. 

PAGE 

Reasons  for  believing  in  its  Existence— Discovery — Its  Satellite. .  256 

CHAPTER  XI. 
THE  PHYSICAL  CONSTITUTION  OF  THE  PLANETS. 

Mercury  and  Venus — The  Earth  and  Mars— Jupiter  and  Saturn 
— Uranus  and  Neptune 261 

CHAPTER  XII. 
METEORS. 

Phenomena  and  Causes  of  Meteors — Meteoric  Showers — Relation 
of  Meteors  and  Comets— The  Zodiacal  Light 265 

CHAPTER  XIIL 
COMETS. 

Aspect  of  Comets— The  Vaporous  Envelopes — Physical  Consti- 
tution— Motions — Remarkable  Comets — Encke's  Comet — 
The  Resisting  Medium 274 


PAET  III. 

INTRODUCTION 285 

CHAPTER  I. 
CONSTELLATIONS. 

General  Aspect  of  the  Heavens — The  Galaxy — Lucid  Stars — 
Telescopic  Stars — Magnitudes  of  the  Stars — The  Constella- 
tions and  Names  of  the  Stars — Numbering  and  Cataloguing 
the  Stars 288 

CHAPTER  II. 

VARIABLE  AND  TEMPORARY  STARS. 
Stars  Regularly  Variable— Temporary  or  New  Stars 296 


X  CONTENTS. 

CHAPTER  m. 

MULTIPLE  STABS. 

Character  of  Double  and  Multiple  Stars— Binary  Systems 301 

CHAPTER  IV. 
NEBULAE  AND  CLUSTERS. 

Discovery  of  Nebulae — Classification  of  Nebulae — Clusters — Star 
Clusters— Spectra  of  Nebulae,  Clusters,  and  Fixed  Stars- 
Motion  of  Stars  in  the  Line  of  Sight 304 

CHAPTER  V. 
MOTIONS  AND  DISTANCES  OF  THE  STARS. 

Proper  Motions— Proper  Motion  of  the  Sun — Distances  of  the 
Fixed  Stars 312 

CHAPTER  VI. 

CONSTRUCTION  OP  THE  HEAVENS. 
Star-gauging— The  Milky  Way 318 

CHAPTER  VII. 

COSMOGONY. 
Laplace's  Nebular  Hypothesis— General  Conclusions 323 

APPENDIX. 

Spectrum  Analysis — The  Spectroscope — The  Solar  Spectrum — 
Results  of  Spectroscopic  Observations — Description  and 
Maps  of  the  Constellations 833 

INDEX .  347 


ASTRONOMY. 


INTRODUCTION. 

Astronomy  Defined. — Astronomy  (affrrfp — a  star,  and 
vof^o? — a  law)  is  the  science  which  has  to  do  with  the 
heavenly  bodies,  their  appearances,  their  nature,  and  the 
laws  governing  their  real  and  their  apparent  motions. 

In  approaching  the  study  of  this  the  oldest  of  the 
sciences  depending  upon  observation,  it  must  be  borne  in 
mind  that  its  progress  is  most  intimately  connected  with 
that  of  the  race,  it  having  always  been  the  basis  of  geog- 
raphy and  navigation,  and  the  soul  of  chronology.  Some 
of  the  chief  advances  and  discoveries  in  abstract  mathe- 
matics have  been  made  in  its  service,  and  the  methods 
both  of  observation  and  analysis  once  peculiar  to  its  prac- 
tice now  furnish  the  firm  bases  upon  which  rest  that  great 
group  of  exact  sciences  which  we  call  Physics. 

It  is  more  important  to  the  student  that  he  should  be- 
come penetrated  with  the  spirit  of  the  methods  of  astron- 
omy than  that  he  should  recollect  its  minutia3 ;  and  it  is 
most  important  that  the  knowledge  which  he  may  gain 
from  this  or  other  books  should  be  referred  by  him  to  its 
true  sources.  For  example,  it  will  often  be  necessary  to 
speak  of  certain  planes  or  circles,  the  ecliptic,  the  equa- 
tor, the  meridian,  etc.,  and  of  the  relation  of  the  appa- 


£  ASTRONOMY. 

rent  positions  of  stars  and  planets  to  them;  but  his  labor 
will  be  useless  if  it  has  not  succeeded  in  giving  him  a  pre- 
cise notion  of  these  circles  and  planes  as  they  exist  in  the 
sky,  and  not  merely  in  the  figures  of  his  text-book.  Above 
all,  the  study  of  this  science,  in  which  not  a  single  step 
could  have  been  taken  without  careful  and  painstaking 
observation  of  the  heavens,  should  lead  its  student  himself 
to  attentively  regard  the  phenomena  daily  and  hourly  pre- 
sented to  him  by  the  heavens. 

Does  the  sun  set  daily  in  the  same  point  of  the  horizon? 
Does  a  change  of  his  own  station  affect  this  and  other 
aspects  of  the  sky?  At  what  time  does  the  full  moon  rise? 
Which  way  are  the  horns  of  the  young  moon  pointed? 
These  and  a  thousand  other  questions  are  already  answered 
by  the  observant  eyes  of  the  ancients,  who  discovered  not 
only  the  existence,  but  the  motions,  of  the  various  planets, 
and  gave  special  names  to  no  less  than  fourscore  stars. 
The  modern  pupil  is  more  richly  equipped  for  observation 
than  the  ancient  philosopher.  If  one  could  have  put  a 
mere  opera-glass  in  the  hands  of  HIPPARCHUS  the  world 
need  not  have  waited  two  thousand  years  to  know  the 
nature  of  that  early  mystery,  the  Milky  Way,  nor  would  it 
have  required  a  GALILEO  to  discover  the  phases  of  Venus 
and  the  spots  on  the  sun. 

Astronomy  furnishes  the  principles  and  the  methods  by 
means  of  which  thousands  of  ships  are  navigated  with 
safety  and  certainty  from  port  to  port ;  by  which  the 
dimensions  of  the  earth  itself  are  fixed  with  high  precision; 
by  which  the  distances  of  the  sun,  the  planets,  and  the 
brighter  stars  are  measured  and  determined.  The  details 
of  these  methods  cannot  be  given  in  an  elementary  work  ; 
but  the  general  principles  and  even  the  spirit  of  the  special 


INTRODUCTION.  3 

methods  can  be  entirely  mastered  by  the  faithful  student. 
All  the  attention  which  he  can  bring  will  be  richly  reward- 
ed by  the  insight  he  will  gain  into  the  noblest  of  the  physi- 
cal sciences. 

How  to  Study  Astronomy. — There  are  a  few  principles 
of  Mathematics  of  Geography,  of  Physics,  which  must  be 
clearly  understood  by  the  student  commencing  astronomy, 
so  that  he  may  go  on  with  advantage.  They  are  all  quite 
simple,  but  they  must  be  entirely  fixed  in  the  mind,  in 
order  that  the  attention  may  be  directed  to  the  astronomical 
principle  and  not  diverted  by  an  attempt  to  recollect  a  fact 
from  another  science.  Any  patience  and  concentration 
which  the  student  may  bestow  upon  them  at  the  outset 
should  *be  rewarded  by  the  facility  with  which  they  will 
enable  him  to  grasp  the  more  interesting  portions  of  the 
subject.  The  few  definitions  which  are  given  in  italics 
should  be  memorized  in  the  words  of  the  text.  In  all  other 
cases  it  is  preferable  that  the  student  should  give  his  own 
explanations  in  his  own  words. 

First  we  will  go  briefly  over  some  of  the  essential  mathe- 
matical principles  alluded  to. 

Angles :  their  Measurement. — An  angle  is  the  amount 
of  divergence  of  two  right  lines.  For  example,  the  angle 
between  the  two  right  lines  81E  and 
8*E  is  the  amount  of  divergence  of 
these  lines.  The  angle  8*E8*  is  the 
amount  of  divergence  of  the  two  lines 
SSE  and  S*K  The  eye  sees  at  once 
that  the  angle  S3ES*  in  the  figure  is 
greater  than  the  angle  S1ES*,  and 
that  the  angle  8*ES*  is  greater  than 
either  of  them. 


4  ASTRONOMY. 

In  order  to  compare  them  and  to  obtain  their  numerical 
ratio,  we  must  have  a  unit-angle. 

The  unit  angle  is  obtained  in  this  way:  The  circumfer- 
ence of  any  circle  is  divided  into  360  equal  parts.  The 
points  of  division  are  joined  with  the  centre.  The  angles 
between  any  two  adjacent  radii  are  called  degrees.  In  the 
figure,  S'fiS*  is  about  12°,  S'ES*  is  about  22°,  S'ES*  is 
about  30°,  and  Sl£S4  is  about  64°.  The  vertex  of  the 
angle  is  at  the  centre  E ':  the  measure  of  the  angle  is  on 
the  circumference  S1S*S*S',  or  on  any  other  circumference 
drawn  from  E  as  a  centre. 

In  this  way  we  have  come  to  speak  of  the  length  of  one 
three-hundred-and-sixtieth  part  of  any  circumference  as  a 
degree,  because  radii  drawn  from  the  ends  of  this  part 
make  an  angle  of  1°. 

For  convenience  in  expressing  the  ratios  of  different 
angles  we  have  subdivided  the  degree  into  minutes  and 
seconds.  The  degree  is  too  large  a  unit  for  some  of  the 
purposes  of  astronomy,  just  as  the  metre  is  too  large  a  unit 
for  use  in  the  machine-shop,  where  fine  work  is  concerned. 

One  circumference  =  360°  =  21600'  =  1296000* 
1°  =    60'  =  360' 
1'  =    60' 

When  we  wish  to  express  smaller  angles  than  seconds, 
we  use  decimals  of  a  second.  Thus  one-quarter  of  a  second 
is  0*.25;  one  quarter  of  a  minute  is  15'. 

The  Radius  of  the  Circle  in  Angular  Measure. — If  'R  is 
the  radius  of  a  circle,  we  know  from  geometry  that  1  cir- 
cumference =  2  n  R,  where  n  —  3.1416.  That  is, 

2  it  M  -  360°  =  21600'  =  1296000' 
or  R  =  57°.  3  =  3437'.?  =  206264'.  8. 


INTRODUCTION.  5 

By  this  we  mean  that  if  a  flexible  cord  equal  in  length 
to  the  radius  of  any  circle  were  laid  round  the  circumfer- 
ence of  that  circle,  and  if  two  radii  were  then  drawn  to  the 
ends  of  this  cord,  the  angle  of  these  radii  would  be  57°. 3, 
3437'.7,  or  206264". 8. 

It  is  important  that  this  should  be  perfectly  clear  to  the 
student. 

For  instance,  how  far  off  must  you  place  a  foot-rule  in 
order  that  it  may  subtend  an  angle  of  1°  at  your  eye? 
Why,  57.3  feet  away.  How  far  must  it  be  in  order  to  sub- 
tend an  angle  of  a  minute  ?  3437.7  feet.  How  far  for  a 
second  ?  206264.8  feet,  or  over  39  miles. 

Again,  if  an  object  subtends  an  angle  of  1°  at  the  eye, 

we  know  that  its  diameter  must  be  ^-5  as  great  as  its  dis- 

57  .o 

tance  from  us.  If  it  subtends  an  angle  of  1",  its  distance 
from  us  is  over  200,000  times  as  great  as  its  diameter. 

The  instruments  employed  in  astronomy  may  be  used  to 
measure  the  angles  subtended  at  the  eye  by  the  diameters  of 
the  heavenly  bodies.  In  other  ways  we  determine  their  dis- 
tance from  us  in  miles.  A  combination  of  these  data  will 
give  us  the  actual  dimensions  of  these  bodies  in  miles. 
For  example,  the  sun  is  about  93,000,000  miles  from  the 
earth.  The  angle  subtended  by  the  sun's  diameter  at  this 
distance  is  1922*.  What  is  the  diameter  of  the  sun  in  miles  ? 

An  idea  of  angular  dimensions  in  the  sky  may  be  had  by 
remembering  that  the  angular  diameters  of  the  moon  and 
of  the  sun  are  about  30'.  It  is  180°  from  the  west  point  to 
the  east  point  counting  through  the  point  immediately 
overhead.  How  many  moons  placed  edge  to  edge  would  it 
take  to  reach  from  horizon  to  horizon  ?  The  student  may 
guess  at  the  answer  first  and  then  compute  it. 


Q  ASTRONOMY. 

Perhaps  a  more  convenient  measure  is  the  apparent  dis- 
tance apart  of  the  "  pointers"  in  the  Great  Dipper,  which 
is  5°.  (See  Fig.  7,  page  &i.) 

Plane  Triangles. — The  angles  of  which  we  have  been 
speaking  are  angles  in  a  plane.  In  any  plane  triangle  there 
are  three  sides  and  three  angles— six  parts.  If  any  three  of 
these  parts  (except  the  three  angles)  are  given  we  can 
construct  the  triangle.  If  the  three  angles  alone  are  given 
we  can  make  a  triangle  which  shall  be  of  the  right  shape, 
and  that  is  all. 


Fro.  2. 


Spherical  Triangles. — Besides  plane  angles  and  triangles, 
we  have  to  do  with  those  drawn  on  the  surface  of  a  sphere 
— spherical  triangles.  This  is  necessary  since  the  heavenly 
bodies  are  spherical  in  shape,  and  since  they  are  seen  pro- 
jected against  the  concave  surface  of  the  sky. 

The  Sphere:  its  Planes  and  Circles. — In  the  figure,  0  is 
the  centre  of  the  sphere  and  ABE  is  one  of  its  circles. 
Suppose  a  plane  AB  passing  through  the  centre  and  cut- 


INTRODUCTION.  7 

\ 
ting  the  sphere  into  two  hemispheres.     It  will  intersect  the 

surface  of  the  sphere  in  a  circle  AEBF  which  is  called  a 
great  circle  of  the  sphere.  A  great  circle  of  the  sphere  is 
one  cut  from  the  surface  by  a  plane  passing  through  the 
centre  of  the  sphere.  Suppose  a  right  line  POP'  perpen- 
dicular to  this  plane.  The  points  P  and  Pf  in  which  it 
intersects  the  surface  of  the  sphere  are  everywhere  90° 
from  the  circle  AEBF.  They  are  the  poles  of  that  circle. 
The  poles  of  the  great  circle  CEDF  are  Q  and  Q'. 

The  following  relations  exist  between  the  angles  made 
in  the  figure: 

I.  The  angle  POQ  between  the  poles  is  equal  to  the  in- 
clination of  the  planes  to  each  other. 

II.  The  arc  BD  which  measures  the  greatest  distance 
between  the  two  circles  is  equal  to  the  arc  PQ  which 
measures  the  angle  POQ. 

III.  The  points  E  and  F,  in  which  the  two  great  cir- 
cles intersect  each  other,  are  the  poles  of  the  great  circle 
PQACP'Q'BD  which  passes  through  the  poles  of  the  first 
two  circles. 

The  Spherical  Triangle. — In  the  last  figure  there  are 
several  spherical  triangles,  as  EDB,  FAC,  ECP'Q'B,  etc. 
In  astronomy  we  need  consider  only  those  whose  sides 
are  formed  by  arcs  of  great  circles.  The  angles  of  the 
triangle  are  angles  between  two  arcs  of  great  circles;  or  what 
is  the  same  thing,  they  are  angles  between  the  two  planes 
which  cut  the  two  arcs  from  the  surface  of  the  sphere. 

In  spherical  triangles,  as  in  plane,  there  are  six  parts, 
three  angles  and  three  sides.  Having  any  three  parts  the 
other  three  can  be  constructed. 

The  sides  as  well  as  the  angles  of  spherical  triangles  are 
expressed  in  degrees,  minutes,  and  seconds.  If  the  student 


g  ASTRONOMY. 

has  a  globe  before  him,  let  him  mark  on  it  the  triangle 
whose  angles  are 

A  128°  44'  45M, 
B  33°  11' 12'.0, 
G  18°15'31M, 

and  whose  sides  are  (a  is  opposite  to  A,  I  to  B,  c  to  C.) 
a  =  10°,      b  =  7°,      c  =  4°. 

Power  of  the  Eye  to  see  Small  Objects. — When  a  round 
object  subtends  an  angle  of  1'  (that  is,  when  it  is  about 
3437  of  its  own  diameters  away),  it  is  just  at  the  limit  of 
visibility,  under  ordinary  circumstances.  At  the  Transit  of 
Venus  in  1874,  the  planet  Venus  was  between  the  earth 
and  the  sun,  and  appeared  as  a  small  black  spot,  just  visi- 
ble to  the  naked  eye,  projected  on  the  sun's  face.  It  was 
67*  in  diameter. 

If  two  such  discs  are  nearer  together  than  1'  12',  few 
eyes  can  distinguish  them  as  two  distinct  objects.  If  a 
body  is  long  and  narrow,  its  angular  dimensions  (width) 
may  be  reduced  to  10*  or  15*  before  it  is  indistinguishable 
to  the  eye.  For  example,  a  spider  line  hanging  in  the  air. 

If  an  object  is  very  much  brighter  than  the  background 
on  which  it  is  seen,  there  is  no  limit  below  which  it  is  nec- 
essarily invisible.  Its  visibility  depends,  in  such  a  case, 
only  on  its  brightness.  It  is  probable  that  the  diameters 
of  the  brightest  stars  subtend  an  angle  no  greater  than 
O'.Ol. 

Latitude  and  Longitude  of  a  Place  on  the  Earth's  Surface. 
Geography  teaches  us  that  the  earth  is  a  sphere.  Positions 
on  its  surface  are  defined  by  giving  their  latitude  and 
longitude.  According  to  geography,  the  latitude  of  a  place 
on  the  earth's  surface  is  its  angular  distance  north  or  south 
of  the  equator. 


INTRODUGTION.  $ 

The  longitude  of  a  place  on  the  earth's  surface  is  its 
angular  distance  east  or  west  of  a  given  first  meridian, 

If  P  in  the  figure  is  the  north  pole  of  the  earth,  the 
latitude  of  the  point  B  is  60°  north;  of  Z  it  is  30°  north; 
of  /  it  is  27°-J  south.  All  places  having  the  same  latitude 
are  situated  on  the  same  parallel  of  latitude.  In  the  figure 
the  parallels  of  latitude  are  represented  by  straight  lines. 

All  places  having  the  same  longitude  are  situated  on  the 


Fia.  3. 

same  meridian.     "We  shall  give  the  astronomical  definitions 
of  these  terms  further  on. 

It  is  found  convenient  in  astronomy  to  modify  the  geo- 
graphical definition  of  longitude.  In  geography  we  say 
that  Washington  is  77°  west  of  Greenwich,  and  that  Syd- 
ney (Australia)  is  151°  east  of  Greenwich.  For  astro- 
nomical purposes  it  is  found  more  convenient  to  count  the 


10  ASTRONOMY. 

longitude  of  a  place  from  the  first  meridian  (usually 
Greenwich)  always  towards  the  west.  Thus  Sydney  is  209° 
west  of  Greenwich.  360°-151°=209°. 

The  earth  turns  on  its  axis  once  in  24  hours.  In  this 
time  a  point  on  its  surface  moves  through  360  degrees,  or 
such  a  point  moves  at  the  rate  of  15°  per  hour.  360  divided 
by  24  is  15. 

Hence  we  may  express  the  longitude  of  a  place  either  in 
time  or  arc.  Washington  is  5h  8m  west  of  Greenwich,  and 
Sydney  is  13h  56m  west  of  Greenwich. 

It  is  also  indifferent  which  first  meridian  we  choose. 
We  may  refer  all  longitudes  to  Paris,  to  Berlin,  or  to  Wash- 
ington. Sydney  is  8h  48m  west  of  Washington,  and  Green- 
wich is  18h  52m  west  of  Washington. 

In  the  figure,  suppose  F  to  be  west  of  the  first  meridian. 
All  the  places  on  the  straight  line  PQ  have  a  longitude  of 
15°  or  1  hour ;  all  on  the  curve  P5h  Q  have  a  longitude 
of  75°  or  5  hours;  and  so  on. 

The  difference  of  longitude  of  any  two  places  on  the  earth 
is  the  angular  distance  between  the  terrestrial  meridians 
passing  through  the  two  places. 

Thus  Washington  is  77°  west  of  Greenwich,  and  Sydney 
is  209°  west  of  Greenwich.  Hence  Sydney  is  132°  west  of 
Washington,  and  this  is  the  difference  of  longitude  of  the 
two  places. 


SYMBOLS    AND    ABBREVIATIONS 


SIGNS  OP   THE  PLANETS,    ETC. 


©  or 


The  Sun. 
The  Moon. 
Mercury. 
Venus. 
The  Earth. 


Mars. 

Jupiter. 

Saturn. 

Uranus. 

Neptune. 


The  asteroids  are  distinguished  by  a  circle  enclosing  a  number, 
which  number  mdicates  the  order  of  discovery,  or  by  their  names, 
or  by  both,  as  (100)  ;  Hecate. 


Spring   ( 
signs.    } 

Summer  \ 
signs.    ) 

1. 
2. 
3. 
4. 
5. 
6. 

T 
n 
<l 

m 

SIGNS  OF  T 

Aries. 
Taurus. 
Gemini. 
Cancer. 

Virgo. 

HE   ZODIAC. 

Autumn 
signs. 

Winter 

signs. 

!* 

[    9. 
;10. 

!  lle 
!l2. 

=£=  Libra. 
TTL  Scorpius. 
#    Sagittarius. 
V3  Capricornus, 
£?  Aquarius. 
K  Pisces. 

The  Greek  alphabet  is  here  inserted  to  aid  those  who  are  not  already 
familiar  with  it  in  reading  the  parts  of  the  text  in  which  its  letters 
occur : 


Letters. 

Names. 

A  a 

Alpha 

B  ft 

Beta 

rr 

Gamma 

A  S 

Delta 

E  s 

Epsilon 

ZC 

Zeta 

Hrf 

Eta 

050 

Theta 

It 

Iota 

K  K 

Kappa 

A  A 

Lambda 

M  // 

Mu 

Letters. 
N  v 

O  o 

n  TtTt 
PP 

2  6  $ 
T  r 
TV 


Names. 
Nu 
Xi 
Omicron 

Pi 

Rho 

Sigma 

Tau 

Upsilon 

Phi 

Chi 

Psi 

Omega 


12  ASTRONOMY. 


THE    METRIC    SYSTEM. 

THE  metric  system  of  weights  and  measures  being  employed  in 
this  volume,  the  following  relations  between  the  units  of  this  system 
most  used  and  those  of  our  ordinary  one  will  be  found  convenient  for 
reference  : 

MEASURES  OP  LENGTH, 

1  kilometre   =  1000  metres        =    0-62137  mile. 
1  metre          =  the  unit  =  39-370  inches. 

1  millimetre  =  ^fa  of  a  metre  =    0-03937  inctu 


MEASURES  OP  WEIGHT. 


1  kilogramme  =  1000  grammes  =    2-2046  pounds. 
1  gramme        =  the  unit  =  15-432  grains. 


The  following  rough  approximations  may  be  memorized  : 

The  kilometre  is  a  little  more  than  T*ff  of  a  mile,  but  less  than  f  of 
a  mile. 

The  mile  is  lT6ff  kilometres. 
The  kilogramme  is  2\  pounds. 
The  pound  is  less  than  half  a  kilogramme. 
One  metre  is  3-3  feet. 
One  metre  is  39-4  inches. 


CHAPTEB  L 
THE  RELATION  OF  THE  EARTH  TO  THE  HEAVENS. 

THE  EARTH'S  SHAPE  AND  DIMENSIONS. 

The  earth  is  a  globe  whose  dimensions  are  gigantic 
when  compared  with  our  ordinary  and  daily  ideas  of  size. 

Its  shape  is  nearly  a  sphere,  as  has  been  abundantly 
proved  by  the  accurate  geodetic  surveys  which  have  been 
made  by  various  nations. 

Of  its  size  we  may  get  a  rough  idea  by  remembering 
that  at  the  present  time  it  requires  about  three  months  to 
travel  completely  around  it. 

To  these  familiar  facts  we  may  add  two  propositions 
which  are  fundamental  in  astronomy. 

I.  The  earth  is  completely  isolated  in  space.    The  most 
obvious  proof  of  this  is  that  men  have  visited  nearly  every 
part  of  the  earth's  surface  without  finding  anything  to  the 
contrary. 

II.  The  earth  is  one  of  a  vast  number  of  globular  bodies, 
familiarly  known  as  stars  and  planets,  moving  according 
to  certain  laws  and  separated  by  distances  so  immense  that 
the  magnitudes  of  the  bodies  themselves  are  insignificant  in 
comparison  to  these  distances.     The  first  conception  which 
the  student  of  astronomy  has  to  form  is  that  of  living  on 
the  surface  of  a  spherical  earth  which,  although  it  seems  of 
immense  size  to  him,  is  really  but  a  point  in  comparison 


14  ASTRONOMY. 

with  the  distances  which  separate  him  from  the  stars  which 
he  nightly  sees  in  the  sky. 

THE  CELESTIAL  SPHEKE. 

When  we  look  at  a  star  at  night  we  seem  to  see  it  set 
against  the  dark  surface  of  a  holloy  sphere  in  whose  centre 
we  are. 

All  the  stars  seem  to  be  at  the  same  distance  from  us. 
When  we  stop  to  consider,  we  see  that  it  is  quite  possible 
that  some  one  of  the  many  stars  visible  may  be  nearer 
than  some  other,  but  as  we  have  no  immediate  method 
of  knowing  which  of  two  stars  is  the  nearer,  we  are  driven 
to  speak  of  their  apparent  positions  just  as  if  they  were 
bright  points  studded  over  the  inner  surface  of  a  large 
hollow  globe,  and  all  at  the  same  distance  from  us.  The 
radius  of  this  globe  is  unknown.  We  do  not,  however, 
think  of  any  of  the  stars  as  beyond  the  surface  and 
shining  through  it.  We  therefore  suppose  the  radius  of 
the  sphere  to  be  equal  to  or  greater  than  the  distance  of 
the  remotest  star. 

Students  generally  fail  at  the  outset  to  realize  two  very 
important  facts  in  relation  to  the  celestial  sphere.  First, 
that  for  all  the  purposes  of  our  present  knowledge  the 
relative  positions  of  the  stars  on  its  surface  do  not  vary. 
Maps  were  made  of  these  positions  centuries  ago  which  are 
as  correct  now  as  old  maps  of  portions  of  the  earth.  The 
motions  of  the  earth  present  different  portions  of  the  celes- 
tial sphere  to  our  observation  at  different  times,  and  one 
who  has  not  thought  at  all  of  the  subject  might  by  that 
fact  be  led  to  suppose  that  changes  are  taking  place  in  the 
relative  positions  of  the  stars  themselves.  Most  people, 
however,  know  that  they  can  find  the  same  groups  of  stars 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.   15 

— "  constellations, "  as  they  are  called — in  different  direc- 
tions from  the  observer's  location  on  the  earth,  night  after 
night;  the  difference  in  the  directions  being  due  to  the 
earth's  motions.  Reflection  on  the  foregoing  will  help  the 
student  to  realize  the  second  important  fact  alluded  to  in  the 
beginning  of  this  paragraph — that  for  most  practical  pur- 
poses of  astronomy  the  earth  may  be  regarded  as  a  point 


FIG.  4. 

in  the  centre  of  a  hollow  globe  whose  inside  surface  is 
spotted  over  with  the  stars,  that  hollow  globe  corresponding 
to  the  celestial  sphere.  In  fact  ingenious  instruments  to 
illustrate  some  of  the  truths  of  astronomy  have  been  made 
of  large  globes  of  glass  or  other  transparent  substances, 
with  the  stars  painted  in  their  unvarying  positions  on  the 


16  ASTRONOMY. 

inside  surface,  and  the  earth  suspended  at  the  centre  by 
supports  rendered  as  nearly  invisible  as  possible. 

Suppose  an  observer  at  the  point  0  in  the  figure.  If  he 
sees  a  star  at  the  point  Q  it  is  clear  that  the  real  star  may 
be  anywhere  in  space  on  the  line  OQ,  as  at  q  for  example, 
and  still  appear  to  be  at  Q. 

Again,  stars  which  appear  to  be  at  the  points  P,  V,  U, 
T,  S,  R,  may  in  fact  be  anywhere  on  the  lines  OP,  0  V, 
OU,  OT,  OS,  OR.  Thus,  if  there  were  three  stars  along 
the  line  0  T,  they  would  all  be  projected  at  the  point  T  of 
the  celestial  sphere,  and  would  appear  as  one  star. 

The  celestial  sphere  is  the  surface  upon  which  we  im- 
agine the  stars  to  be  projected. 

The  projection  of  a  body  upon  the  celestial  sphere  is  the 
point  in  which  this  body  appears  to  be,  when  seen  from 
the  earth.  This  point  is  also  called  the  apparent  position 
of  the  body.  Thus  to  an  observer  at  0,  T  is  the  apparent 
position  of  any  of  the  stars  whose  true  positions  are  t,  t,  t. 
Hence  it  follows  that  positions  on  the  celestial  sphere  re- 
present the  directions  of  the  heavenly  bodies  from  the  ob- 
server, but  have  no  necessary  relation  to  their  distances. 

If  the  observer  changes  his  position,  the  apparent  posi- 
tions of  the  stars  will  also  change. 

We  need  some  method  of  describing  the  apparent  posi- 
tions of  stars  on  the  celestial  sphere;  to  do  this  we  im- 
agine a  number  of  great  circles  to  be  drawn  on  its  surface, 
and  to  these  circles  we  refer  the  apparent  positions  of  the 
stars. 

A  consideration  of  Fig.  2  will  show  the  correctness  of 
the  following  propositions,  which  it  is  necessary  should  be 
clearly  understood: 

I,  Every  straight  line  through  the  observer,  when  pro- 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.   17 

duced  indefinitely,  intersects  the  celestial  sphere  in  two 
opposite  points. 

II.  Every  plane   through   the  observer  intersects  the 
sphere  in  a  great  circle. 

III.  For  every  such  plane  there  is  one  line  through  the 
observer's  position  which    intersects   the    plane  at  light 
angles.     This  line  meets  the  sphere  at  the  poles  of  the 
great  circle  which  is  cut  from  the  sphere  by  the  plane. 

Example:  P  P' ,  Fig.  2,  is  a  line  through  0  perpendicular 
to  the  plane  A  B.  P,  P'  are  the  poles  of  A  B. 

IV.  Every  line  through  the  centre  has  one  plane  perpen- 
dicular to  it,  which  plane  cuts  the  sphere  in  a  great  circle 
whose   poles  are   the  intersection    of    the    line  with  the 
sphere. 

Example:  The  Hue  Q  Q'  has  one  plane  C D  through  0 
perpendicular  to  it,  and  only  this  one. 

THE  HORIZON. 

A  level  plane  touching  the  spherical  earth  at  the  point 
where  an  observer  stands  is  called  the  horizon  of  that 
observer. 

This  plane  cuts  the  celestial  sphere  in  a  great  circle, 
which  is  called  the  celestial  horizon.  The  celestial  horizon 
is  therefore  the  boundary  between  the  visible  and  the  in- 
visible hemispheres  to  that  observer. 

The  Vertical  Line. — The  vertical  Jine  of  any  observer  is 
the  direction  of  a  plumb-line  where  he  stands.  This  line 
is  perpendicular  to  his  horizon.  It  intersects  the  celestial 
sphere  in  two  points,  called  the  zenith  and  the  nadir  of 
that  observer^ 

The  zenith  of  an  observer  is  thejpoint  where  his  vertical 
line  cuts  the  celestial  sphere  above  his  head. 


18  ASTRONOMY. 

The  nadir  of  an  observer  is  the  point  where  his  vertical 
line  cuts  the  celestial  sphere  below  his  feet. 

The  zenith  and  nadir  are  the  poles  of  the  horizon. 
Vertical  Planes  and  Circles. — A  vertical  plane  with  re- 
spect to  any  observer  is  a  plane  which  contains  his  vertical 
line.     It  must  pass  through  his  zenith  and  nadir  and  must 
be  perpendicular  to  his  horizon. 

A  vertical  plane  cuts  the  celestial  sphere  in  a  vertical 
circle. 

As  soon  as  we  imagine  an  observer  to  be  at  any  point  on 

the  earth's  surface  bis  horizon 
is  at  once  fixed;  bis  zenith 
and  nadir  arc  also  fixed.  From 
his  zenith  radiate  a  -number 
of  vertical  circles  which  cut  the 
celestial  horizon  perpendicu- 
larly, and  unite  again  at  his 
nadir.  This  is  a  system  of 
lines  and  circles  which  every 
.  5.  person  carries  about  with 

him,  as  it  were,  and  which   may  serve  him  for  lines  to 
which  to  refer  the  apparent  position  of  every  star  which  he 


Some  one  of  these  vertical  circles  will  pass  through  any 
and  every  star  visible  to  this  observer. 
v  The  altitude  of  a  heavenly  body  is  its  elevation  above  the 
plane  of  the  horizon  measured  on  a  vertical  circle  through 
the  star. 

The  zenith  distance  of  a  star  is  its  angular  distance  from 
the  zenith  measured  on  a  vertical  circle. 

In  the  figure,  Z 8  is  the  zenith  distance  (£)  of  S,  and 
(a)  is  its  altitude.     Z  S  H  is  an  arc  of  a  great  circle; 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.   19 

the  vertical  circle  through  the  star.  ZS  H  =  a  -f  £  =  90°, 
and  <?  =  90°  -  a  or  a  =  90°  -  <?. 

The  altitude  of  a  star  in  the  zenith  is  90°;  half  way  from 
the  zenith  to  the  horizon  it  is  45°;  in  the  horizon  it  is  0°. 

T/ie  azimuth  of  a  star  is  the  angular  distance  from  the  point 
where  the  vertical  circle  through  it  meets  the  horizon,  to  the 
north  (or  south)  point  of  the  horizon. 

In  the  figure,  NH  is  the  azimuth  of  8.  The  azimuth 
of  a  star  in  the  east  or  west  is  90°. 

The  prime  vertical  of  an  observer  is  that  one  of  his  verti- 
cal circles  which  passes  through  his  east  and  west  points. 

Co-ordinates  of  a  Star. — The  apparent  position  of  a  heav- 
enly body  is  completely  fixed  by  means  of  its  altitude  and 
azimuth.  If  we  know  the  altitude  and  azimuth  of  a  star 
we  can  point  to  it. 

If,  for  example,  its  azimuth  is  20°  from  north  towards 
the  west  and  if  its  altitude  is  30°,  we  can  point  to  the  star  by 
measuring  an  angle  of  20°  from  the  north  point  towards 
the  west,  which  will  fix  the  foot  of  a  vertical  circle  through 
the  star.  The  star  itself  will  be  on  the  vertical  circle,  30° 
above  the  horizon. 

This  point,  and  this  alone,  will  correspond  to  the  posi- 
tion of  the  star  as  determined  by  its  altitude  and  azimuth. 

Numbers  (or  quantities)  which  exactly  define  the  position 
of  a  body  are  called  its  co-ordinates. 

Hence  altitude  and  azimuth  form  a  pair  of  co-ordinates 
which  fix  the  apparent  position  of  a  star  on  the  celestial 
sphere. 

It  must  be  remembered  that  these  two  co-ordinates  give 
only  the  position  of  the  projection  of  the  star  on  the  celes- 
tial sphere,  and  give  no  knowledge  of  its  distance  from  the 
observer.  The  body  may  be  any  where  on  the  line  defined 


20  ASTRONOMY. 

by  the  position  on  the  celestial  sphere  and  the  place  of  the 
observer. 

If  we  also  know  the  distance  of  the  star  from  the  obser- 
ver, we  know  every  possible  fact  as  to  its  place  in  space. 

Thus,  three  co-ordinates  suffice  to  fix  the  absolute  position 
of  a  body  in  space  ;  two  co-ordinates  suffice  to  determine  its 
apparent  position  on  the  celestial  sphere. 

These  propositions  suppose  the  place  of  the  observer  to 
be  fixed,  since  the  altitude  and  azimuth  refer  to  an  obser- 
ver in  some  one  definite  position.  If  the  observer  should 
change  his  place,  the  star  remaining  fixed,  the  apparent 
position  of  the  star  on  the  celestial  sphere  would  change  to 
him,  owing  to  his  own  motion.  The  numbers  which  ex- 
press this  apparent  position — the  altitude  and  azimuth  of 
the  star — would  also  change. 

But  wherever  the  observer  is,  if  he  has  these  two  co- 
ordinates for  a  star,  the  apparent  place  of  the  star  is  fixed 
for  him. 

The  Horizon. — Since  the  earth  is  spherical  in  form,  and 
the  horizon  is  a  plane  touching  this  sphere,  every  different 
place  must  have  a  different  horizon.  Wherever  an  observer 
goes  on  the  earth's  surface  he  carries  an  horizon,  a  zenith, 
and  a  nadir  with  him,  and  a  set  of  vertical  circles  to  which 
he  can  refer  the  positions  of  all  the  stars  he  sees.  If  lie 
stays  at  a  fixed  point  on  the  earth's  surface  his  horizon  is 
always  fixed  with  relation  to  his  vertical  line.  But  the 
earth  on  which  he  stands  is  turning  round  its  axis,  and  his 
horizon  being  tangent  to  the  earth  is  moving  also  v  and  the 
vertical  line  moves  with  ifo  The  stars  stay  in  the  same  abso- 
lute places  from  year  to  year.  The  earth  on  which  the 
observer  stands  is  turning  round  from  west  to  east.  His 
horizon  is  thus  brought  successively  to  the  east  of  the  various 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.  21 

stars,  which  thus  appear  to  rise  higher  and  higher  above 
it. 

The  earth  continues  its  motion,  and  the  plane  of  his  ho- 
rizon finally  approaches  the  same  stars  from  the  west  and 
they  set  below  it,  only  to  repeat  this  phenomenon  with 
every  rotation  of  the  earth. 

The  horizon  appears  to  each  observer  to  be  the  stable 
thing,  and  the  motion  is  referred  to  the  stars.  As  a  matter 
of  fact  it  is  the  stars  that  stand  still  and  the  horizon  which 
moves  below  them,  causing  them  to  appear  to  rise,  and  then 
above  them,  causing  them  to  appear  to  set. 

THE  DUTBNAL  MOTION. 

/  The  diurnal  motion  is  that  apparent  motion  of  the  sun, 
moon,  and  stars  from  east  to  west  in  consequence  of  which 
they  rise  and,  set> 

We  call  it  the  diurnal  motion  because  it  repeats  itself 
from  day  to  day.  The  diurnal  motion  is  caused  by  a  daily 
rotation  of  the  earth  on  an  axis  passing  through  its  centre 
called  the  axis  of  the  earth. 

This  axis  intersects  the  earth's  surface  in  two  opposite 
points  called  the  north  and  south  poles  of  the  earth.  If  the 
earth's  axis  be  prolonged  in  both  directions,  it  meets  the 
celestial  sphere  in  two  points  which  are  called  the  poles  of 
the  celestial  sphere  or  the  celestial  poles.  The  north  celes- 
tial pole  corresponds  to  the  north  end  of  the  earth's  axis; 
the  south  celestial  pole  to  the  south  end. 

The  plane  of  the  equator  is  that  plane  which  passes 
through  the  earth's  centre  perpendicular  to  its  axis.  This 
plane  intersects  the  earth's  surface  in  a  great  circle  of  the 
earth's  sphere  which  is  called  the  earth's  equator  (e  q  in 
Fig.  6). 


22  ASTRONOMY. 

^ 

This  plane  intersects  the  celestial  sphere  in  a  great  circle 
of  this  sphere  which  is  called  the  celestial  equator  or  equi- 
noctial (EQ  in  Fig.  6). 

The  celestial  equator  is  everywhere  half  way  between  the 
two  celestial  poles  and  thus  90°  from  each.  The  celestial 
poles  are  thus  the  poles  of  the  celestial  equator. 

Apparent  Diurnal  Motion  of  the  Celestial  Sphere. — The 


Fio.6. 


observer  on  the  earth  is  unconscious  of  its  rotation,  and 
the  celestial  sphere  appears  to  him  to  revolve  from  east  to 
west  around  the  earth,  while  the  earth  appears  to  remain 
at  rest.  The  case  is  much  the  same  as  if  he  was  on  a 
steamer  which  is  turning  round,  and  as  if  he  saw  the  har- 
bor-shores, the  ships,  and  the  houses  apparently  turning  in 
an  opposite  direction, 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.  23 

So  far  as  appearances  are  concerned,  it  is  quite  the  same 
thing  whether  we  conceive  the  earth  to  be  at  rest  and  the 
heavens  to  turn  about  it,  or  whether  we  conceive  the  stars 
to  remain  at  rest  and  the  earth  to  move  on  its  axis.  We 
can  explain  all  the  phenomena  of  the  diurnal  motion  in 
either  way.  We  must,  however,  remember  that  it  really  is 
the  earth  which  turns  on  its  axis  and  successively  presents 
to  the  observer  different  parts  of  the  celestial  sphere.  The 
parts  to  his  east  are  just  coming  into  view  (rising  above  his 
horizon).  The  parts  to  his  west  are  about  to  disappear, 
(setting  below  his  horizon). 

Since  the  diurnal  motion  is  an  apparent  rotation  of  the 
celestial  sphere  about  a  fixed  axis,  it  follows  that  there 
must  be  two  points  of  this  sphere  that  remain  at  rest; 
namely,  the  two  celestial  poles.  Moreover,  since  the  celes- 
tial poles  are  opposite  points,  one  pole  must  be  above  the 
horizon  and  therefore  a  visible  point  of  this  sphere,  and 
the  other  pole  must  be  below  the  horizon  and  therefore  in- 
visible. 

The  celestial  pole  visible  to  observers  in  the  northern 
hemisphere  is  the  north  pole.  To  locate  its  place  in  the 
sky  let  the  student  look  at  the  northern  sky  on  any  clear 
evening. 

He  will  see  the  stars  somewhat  as  they  are  represented  in 
the  figure. 

In  fact  Fig.  7.  shows  the  stars  as  they  will  appear  to 
an  observer  -in  the  month  of  August  in  the  early  hours  of 
the  evening.  But  the  configurations  of  the  stars  can  be 
recognized  at  any  other  time. 

The  first  star  to  be  identified  is  Polaris,  or  the  Pole  Star. 
It  may  be  found  by  means  of  the  Pointers,  two  stars  in  the 
constellation  Ursa  Major,  familiarly  known  as  the  Great 


24  ASTRONOMY. 

Dipper.  The  straight  line  through  theae  stare,  as  shown 
in  the  figure,  passes  near  Polaris.  Polaris  is  1±  degrees 
from  the  true  pole.  There  is  no  star  exactly  at  the  pole 
itself. 

The  altitude  of  the  pole-star  above  the  horizon  of  any 
place  is  equal  to  the  latitude  of  the  place,  as  will  be  shown 


Fio.  7. 


hereafter.  Hence  in  most  parts  of  the  United  States  the 
north  pole  is  from  30°  to  45°  above  the  horizon.  In  Eng- 
land it  is  51°,  in  Norway  60°. 

The  north-polar  distance  of  a  star  is  its  angular  distance 
from  the  north  celestial  pole. 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.  25 

The  following  laws  of  the  diurnal  motion  will  now  be 
clear: 

I.  Every  star  in  the  heavens  appears  to  describe  a  circle 
around  the  pole  as  a  centre  in  consequence  of  the  diurnal 
motion. 

II.  The  greater  the  star's,  north-polar  distance  the  larger 
is  the  circle% 

III.  All- the  stars -describe  their  diurnal  orbits  in  the 
same  interval  of  time,  which  is  the  time  required  for  the 
earth  to  turn  once  on  its  axis. 

The  circle  which  &  star  appears  to  describe  in  the  sky  in 
consequence  of  the  diurnal  motion  of  the  earth  is  called  the 
diurnal  orbit  of  that  star. 

These  law*  can  be  proved  by  observation.  The  student 
can  satisfy  himself  of  their  correctness  in  any  clear  night. 

If  the  star's  north-polar  distance  is  less  than  the  altitude 
of  the  pole,  the  circle  which  the  star  describes  will  not 
meet  the  horizon  at  all,  and  the  star  will  therefore  neither 
rise  nor  set,  but  will  simply  perform  an  apparent  diurnal 
revolution  round  the  pole.  Such  stars  are  shown  in  the 
figure.  The  apparent  diurnal  motion  of  the  stars  is  in  the 
direction  shown  by  the  arrows  in  the  cut.  Below  the 
pole  the  stars  appear  to  move  from  left  to  right,  west  to 
east;*  above  the  pole  they  appear  to  move  from  east  to 
west. 

The  circle  within  which  the  stars  neither  rise  nor  set  is 
called  the  circle  of  perpetual  apparition.  The  radius  of 
this  circle  is  equal  to  the  altitude  of  the  pole  above  the 
horizon,  or  to  the  north  polar  distance  of  the  north  point 
of  the  horizon. 

As  a  result  of  this  apparent  motion  each  individual  con- 
stellation changes  its  configuration  with  respect  to  the 


26  ASTRONOMY. 

horizon.  That  part  of  the  constellation  which  is  highest 
when  the  group  is  above  the  pole  becomes  lowest  when  it 
is  below  the  pole.  This  is  shown  in  the  figure,  which 
represents  a  supposed  constellation  at  different  times  of  the 
night  as  it  revolves  round  the  pole.  The  culmination  of  a 
star  occurs  when  it  is  at  its  highest  point  above  the  hori- 
zon. The  point  of  culmination  is  midway  between  the 
points  of  rising  and  setting. 

If  the  polar  distance  of  a  star  exceeds  the  altitude  of  the 


NORTH 

FIG.  8. 

pole,  the  star  will  dip  below  the  horizon  for  a  part  of  its 
diurnal  orbit,  and  the  greater  the  polar  distance  of  the 
star  the  longer  it  will  be  below  the  horizon. 

A  star  whose  polar  distance  is  90°  lies  on  the  celestial 
equator,  and  one  half  of  its  diurnal  orbit  is  above  and 
one  half  below  the  horizon. 

The  sun  is  in  the  celestial  equator  about  March  21st  and 
September  21st  of  each  yeai,  so  that  at  these  times  the 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.  27 

days  and  nights  are  of  equal  length.  This  is  why  the 
celestial  equator  was  formerly  called  the  equinoctial. 

Looking  further  south  at  the  celestial  sphere,  we  shall 
see  stars  which  rise  a  little  to  the  east  of  the  south  point  of 
the  horizon  and  set  a  little  to  the  west  of  this  point,  being 
1  above  the  horizon  but  a  short  time.  The  south  pole  is  as 
far  below  the  horizon  of  any  place  as  the  north  pole  is  above 
it.  Hence  stars  near  the  south  pole  never  rise  in  our 
latitudes.  The  circle  within  which  stars  never  rise  is  called 
the  circle  of  perpetual  occultation. 

It  is  clear  that  the  positions  of  the  circles  of  perpetual 
apparition  and  occultation  depend  upon  the  position  of  the 
observer  upon  the  earth,  and  hence  that  they  will  change 
"their  positions  as  the  observer  changes  his. 

By  going  to  Florida  we  may  see  groups  of  stars  which 
are  not  visible  in  the  latitude  of  New  York. 

The  Meridian. — The  plane  ofjhe  meridian  of  an  observer 
is  that  one  of  his  vertical  planes  which  contains  the  earth's 
axis.  Being  a  vertical  plane  it  must  contain  the  zenith 
and  nadir  of  the  observer ;  as  it  contains  the  earth's  axis 
it  must  contain  the  north  and  south  celestial  poles. 

Different  observers  have  different  meridian  planes,  since 
they  have  different  zeniths. 

The  terrestrial  meridian  of  an  observer  is  the  line  in 
which  the  plane  of  his  meridian  intersects  the  surface  of 
the  earth.  It  is  his  north  and  south  line. 

It  follows  that  if  several  observers  are  due  north  and 
south  of  each  other,  they  have  the  same  terrestrial  meridian. 

The  celestial  meridian  of  an  observer  is  the  great  circle 
cut  from  the  celestial  sphere  by  the  plane  of  that  observer's 
meridian.  Persons  on  the  same  terrestrial  meridian  have 
the  same  celestial  meridian. 


28  ASTRONOMY. 

Terrestrial  meridians  are  considered  as  belonging  to  the 
places  through  which  they  pass.  For  example,  we  speak 
of  the  meridian  of  Greenwich  or  of  the  meridian  of  Wash- 
ington, and  by  this  we  mean  the  (terrestrial  or  celestial) 
meridian  lines  cut  out  by  the  meridian  plane  of  the  Royal 
Observatory  at  Greenwich  or  the  Naval  Observatory  at 
Washington. 

THE  DITTRNAL  MOTION  IN  DIFFERENT  LATITUDES. 

As  we  have  seen,  the  celestial  horizon  of  an  observer  will 
change  its  place  on  the  celestial  sphere  as  the  observer  travels 


Fio.  9.    THB  PARALLEL  SPHERE. 

from  place  to  place  on  the  surface  of  the  earth.  If  he 
moves  directly  toward  the  north  his  zenith  will  approach  the 
north  pole;  but  as  the  zenith  is  not  a  visible  point,  the 
motion  will  be  naturally  attributed  to  the  pole,  which  will 
seem  to  approach  the  point  overhead.  The  new  apparent 
position  of  the  pole  will  change  the  aspect  of  the  observer's 
sky,  as  the  higher  the  pole  appears  above  the  horizon  the 


RELATION  OP  THE  EARTH  10  THE  HEAVENS.  29 

greater  the  circle  of  perpetual  apparition,  and  therefore  the 
greater  the  number  of  stars  which  never  set. 

If  the  observer  is  at  the  north  pole  his  zenith  and  the 
pole  itself  will  coincide  :  half  of  the  stars  only  will  be  vis- 
ible, and  these  will  never  rise  or  set,  but  appear  to  move 
around  in  circles  parallel  to  the  horizon.  The  horizon  and 
the  celestial  equator  will  coincide.  The  meridian  will  be 
indeterminate  since  Z  and.  P  coincide;  there  will  be  no  east 
and  west  line,  and  no  direction  but  south.  The  sphere  in 
this  case  is  called  &  parallel  sphere.  (See  Fig.  9.) 


FIG.  10.— THE  RIGHT  SPHERE. 

If  instead  of  travelling  to  the  north  the  observer  should 
go  toward  the  equator,  the  north  pole  would  seem  to  ap- 
proach his  horizon.  When  he  reached  the  equator  both 
poles  would  be  in  the  horizon,  one  north  and  the  other 
south.  All  the  stars  in  succession  would  then  be  visible, 
and  each  would  be  an  equal  time  above  and  below  the 
horizon.  (See  Fig.  10.) 

The  sphere  in  this  case  is  called  a  right  sphere,  because 
the  diurnal  motion  is  at  right  angles  to  the  horizon.  If 


30  ASTRONOMY. 

now  the  observer  travels  southward  from  the  equator,  the 
south  pole  will  become  elevated  above  his  horizon,  and  in 
the  southern  hemisphere  appearances  will  be  reproduced 
which  we  have  already  described  for  the  northern,  except 
that  the  direction  of  the  motion  will,  in  one  respect,  be 
different.  The  heavenly  bodies  will  still  rise  in  the  east 
and  set  in  the  west,  but  those  near  the  equator  will  pass 
north  of  the  zenith  instead  of  south  of  it,  as  in  our  lati- 
tudes. The  sun,  instead  of  moving  from  left  to  right, 
there  moves  from  right  to  left.  The  bounding  line  be- 
tween the  two  directions  of  motion  is  the  equator,  where 
the  sun  culminates  north  of  the  zenith  from  March  till 
September,  and  south  of  it  from  September  till  March. 

If  the  observer  travels  west  or  east  of  his  first  station, 
his  zenith  will  still  remain  at  the  same  angular  distance 
from  the  north  pole  as  before,  and  as  the  phenomena 
caused  by  the  earth's  diurnal  motion  at  any  place  depend 
only  upon  the  altitude  of  the  elevated  pole  at  that  place, 
these  will  not  be  changed  except  as  to  the  times  of  their 
occurrence.  A  star  which  appears  to  pass  through  the 
zenith  of  his  first  station  will  also  appear  to  pass  through 
the  zenith  of  the  second  (since  each  star  remains  at  a  con- 
stant angular  distance  from  the  pole),  but  later  in  time, 
since  it  has  to  pass  through  the  zenith  of  every  place  be- 
tween the  two  stations.  The  horizons  of  the  two  stations 
will  intercept  different  portions  of  the  celestial  sphere  at 
any  one  instant,  but  the  earth's  rotation  will  present  the 
same  portions  successively,  and  in  the  same  order,  at  both. 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.   31 


CORRESPONDENCE  OF  THE  TERRESTRIAL  AND  CELESTIAL 
SPHERES. 

We  have  seen  that  the  altitude  of  the  pole  above  the 
horizon  of  any  observer  changes  as  the  observer  changes 
his  place  on  the  earth's  surface.  The  exact  relation  of  the 
altitude  of  the  pole  and  the  horizon  of  any  observer  is 
expressed  in  the  following  THEOREM:  The  altitude  of  the 
celestial  pole  above  the  horizon  of  any  place  on  the  earth's 
surface  is  equal  to  the  lati- 
tude of  that  place. 

Let  L  be  a  place  on  the 
earth  P  Ep  Q,  Pp  being 
the  earth's  axis  and  E  Q  its 
equator.  Z  is  the  zenith  of 
the  place,  and  H R  its  hori- 
zon. L  0  Q  is  the  latitude 
of  L  according  to  ordinary 
geographical  definitions;  i.e., 
it  is  the  angular  distance  of 
L  from  the  equator.  Pro- 
long OP  indefinitely  to  P'  FIG.  n. 
and  draw  L  P"  parallel  to  it.  P'  and  P"  are  points  on 
the  celestial  sphere  infinitely  distant  from  L.  In  fact 
they  appear  as  one  point  since  the  dimensions  of  the  earth 
are  vanishingly  small  compared  with  the  radius  of  the 
celestial  sphere,  which  may  be  taken  as  large  as  we  please. 
We  have  then  to  prove  that  L  0  Q  =  P"  L  H.  P  OQ 
and  Z  L  Hare  right  angles,  and  therefore  equal.  Z  LP" 
=  ZOP'  by  construction.  Hence  ZLH-ZLP"  = 
P  0  Q  -  Z  0  P',  or  the  latitude  of  the  point  L  is  meas- 
ured by  either  of  the  equal  angles  L  0  Q  or  P 


32  ASTRONOMY. 

If  we  denote  the  latitude  by  cp  it  follows  that  the  N.P.D. 
(north-polar  distance)  of  Z  is  90°  -  (p.  As  an  observer 
moves  to  various  parts  of  tKe  earth,  his  zenith  changes 
position  with  him.  In  every' position  the  N.P.D.  of  his 
zenith  is  90°  —  <p.  If  he  is  at  the  equator  his  cp  is  0°  and 
his  zenith  is  90°  from  the  north  pole,  which  must  there- 
fore be  in  his  horizon.  If  he  is  at  the  north  pole,  q>  =  -|- 
90°  and  the  N.P.D.  of  his  zenith  is  0°,  or  his  zenith  co- 
incides with  the  north  pole.  If  he  is  at  the  south  pole 
(cp  =  -  90°)  the  N.P.D.  of  his  zenith  is  90°  -  (-  90°) 
or  180°.  That  is,  his  zenith  is  180°  from  the  north  pole, 
or  it  must  coincide  with  the  south  pole ;  and  so  in  other 
cases. 

All  this  has  just  been  shown  (pages  28-30)  in  another 
way,  but  it  is  of  the  first  importance  that  it  should  be  not 
only  clear  but  familiar  to  the  student.  When  he  sees  any 
astronomical  diagram  in  which  the  north  pole  and  the  hori- 
zon are  laid  down  he  can  at  once  tell  for  what  latitude  this 
diagram  is  constructed.  The  elevation  of  the  pole  above 
the  horizon  measures  the  latitude  of  the  observer,  to  whose 
station  this  particular  diagram  applies. 

Change  of  the  Position  of  the  Zenith  of  an  Observer  by 
the  Diurnal  Motion. — In  Fig.  12  suppose  n  e  s  q  to  repre- 
sent the  earth  and  NE  S  Q  the  celestial  sphere.  The  earth, 
as  we  know,  is  rotating  on  the  axis  N  S.  We  have  now  to 
inquire  what  are  the  real  circumstances  of  this  motion. 
The  apparent  phenomena  have  been  previously  described. 
Eemember  that  the  vertical  line  of  an  observer  is  (practi- 
cally) that  of  a  radius  of  the  earth  passing  through  his 
station.  If  the  observer  is  at  n  his  zenith  is  at  N  P. 
If  he  is  at  s  his  zenith  is  at  S  P.  If  the  observer 
ig  in  45°  north  latitude,  he  is  carried  round  by  the 


RELATION  OF   THE  EARTH  TO  THE  HEAVENS.    33 

rotation  of  the  earth  in  a  small  circle  of  the  earth's  surface 
whose  plane  is  perpendicular  to  the  earth's  axis.  This  is 
the  parallel  of  45°,  so  called,^nd  is  indicated  in  the  figure. 
His  zenith  is  always  directly^bove  him,  and  therefore  his 
zenith  must  describe  each  day  a  circle  M  L  on  the  celestial 
sphere  corresponding  to  this  parallel  on  the  earth;  that  is, 


Fio.  12. 

a  circle  half  way  between  the  celestial  pole  and  the  celestial 
equator.  Now,  suppose  the  observer  to  be  on  the  equator 
e  q.  His  zenith  will  then  be  90°  from  either  pole.  As  the 
earth  revolves  on  its  axis  his  zenith  will  describe  a  great 
circle  E  Q  on  the  celestial  sphere.  This  circle  is  the  celestial 
equator.  An  observer  at  45°  south  latitude  will  ha*ve  a 


34  ASTRONOMY. 

parallel  SO  marked  out  on  the  celestial  sphere  by  the 
motion  of  his  zenith  due  to  the  earth's  rotation,  and  so  on. 
Thus,  for  each  parallel  of  la^ude  on  the  earth  we  have  a 
corresponding  circle  on  th«celestial  sphere,  and  each  of 
these  latter  circles  has  its  poles  at  the  celestial  poles. 

Not  only  are  there  circles  of  the  celestial  sphere  which 
correspond  to  parallels  of  latitude  on  the  earth,  but  there 
are  also  celestial  meridians  corresponding  to  the  various 
terrestrial  meridians.  The  plane  of  the  meridian  of  any 
place  contains  the  zenith  of  that  place  ;md  the  two  celestial 
poles.  It  cuts  from  the  earth's  surface  the  terrestrial 
meridian  and  from  the  celestial  sphere  that  great  circle 
which  we  have  defined  as  the  celestial  meridian.  To  fix 
the  ideas  let  us  suppose  an  observer  at  some  one  point  of 
the  earth's  surface.  A  north  and  south  line  on  the  earth 
at  that  point  is  the  visible  representative  of  his  terrestrial 
meridian.  A  plane  through  the  centre  of  the  earth  and 
that  line  contains  his  zenith,  and  cuts  from  the  celestial 
sphere  the  celestial  meridian.  As  the  earth  rotates  on  its 
axis  his  zenith  moves  around  the  celestial  sphere  in  a 
parallel  as  Z L  in  the  last  figure.  Suppose  that  the  east 
point  is  in  front  of  the  picture,  the  west  point  being  be- 
hind it.  Then  as  the  earth  rotates  the  zenith  Z  will  move 
along  the  line  Z  L  from  Z  towards  L.  The  celestial  meri- 
dian always  contains  the  celestial  poles  and  the  point  Z, 
wherever  it  may  be.  Hence  the  arcs  of  great  circles  join- 
ing N.P.  and  S.P.  in  the  figure  are  representatives  of  the 
celestial  meridian  of  this  observer,  at  different  times  dur- 
ing the  period  of  the  earth's  rotation.  They  have  been 
drawn  to  represent  ;the  places  of  the  meridian  at  intervals 
of  1  hour*  That  is,  12  of  them  are  drawn  to  represent 
12  consecutive  positions  of  the  meridian  during  a  semi- 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.    35 

revolution  of  the  earth.  In  this  time  Z  moves  from  Z  to 
L.  In  the  next  semi-revolution  Z  moves  from  L  to  Z, 
along  the  other  half  of  the  parallel  Z  L.  In  24  hours 
the  zenith  Z  of  the  observer  has  moved  from  Z  to  L  and 
from  L  back  to  Z  again.  The  celestial  meridian  has  also 
swept  across  the  heavens  from  the  position  N.P.,  Z,  Q,  S, 
8.  P.  through  every  intermediate  position  to  N.P.,  L,  E,  0, 
.,  and  from  this  last  position  back  to  N.P.,  Z,  Q,  8, 
8.  P.  The  terrestrial  meridian  of  the  observer  has  been 
under  it  all  the  time.  This  real  revolution  of  the  celestial 
meridian  is  incessantly  repeated  with  every  revolution  of 
the  earth.  The  sky  is  studded  with  stars  all  over  the 
sphere.  The  celestial  meridian  of  any  place  approaches 
these  various  stars  from  the  west,  passes  them,  and  leaves 
them.  This  is  the  real  state  of  things.  Apparently  the 
observer  is  fixed.  His  terrestrial  and  celestial  meridians 
seem  to  him  to  be  fixed,  not  only  with  reference  to  himself, 
as  they  are,  but  to  be  fixed  in  space.  The  stars  appear  to 
him  to  approach  his  celestial  meridian  from  the  east,  to 
pass  it,  and  to  move  away  from  it  towards  the  west. 
When  a  star  crosses  the  celestial  meridian  it  is  said  to 
culminate.  The  pa-sage  of  the  star  across  the  meridian  is 
called  the  transit  of  that  star.  This  phenomenon  takes 
place  successively  for  each  observer  on  the  earth.  Suppose 
two  observers,  A  and  B,  A  being  one  hour  (15°)  east  of 
B  in  longitude.  This  means  that  the  angular  distance  of 
their  terrestrial  meridians  is  15°  (see  page  10).  From  what 
we  have  just  learned  it  follows  that  their  celestial  meri- 
dians are  also  15°  apart.  When  B's  meridian  is  N.P., 
Z,  Q,  R,  S.P.,  A's  will  be  the  first  one  (in  the  figure) 
beyond  it;  when  B's  meridian  has  moved  to  this  first  posi- 
tion, A's  will  be  in  the  second,  and  so  on,  always  15° 


36  ASTRONOMY. 

(1  hour)  in  advance.  A  group  of  stars  which  has  just  come 
to  A's  meridian  will  not  pass  B's  for  1  hour.  When  they 
are  on  B's  meridian  they  will  be  1  hour  west  of  A's,  and 
so  on.  Notice  also  that  A's  zenith  is  always  15°  east  of 
B's. 

The  same  stars  will  successively  rise,  culminate,  and  set 
to  each  observer,  but  the  phenomena  will  be  presented  to 
the  eastern  observer  sooner  than  to  the  other. 


FIG.  12«. 

If  N  be  the  earth,  and  a  a  spectator  whose  zenith  is  at 
Z  &t  the  instant  chosen  for  making  the  picture,  and  Z',  Z" 
at  subsequent  times,  his  horizon  must  successively  take  the 
positions  H,  H',  H".  .  .  The  stars  near  E  (the  east  point) 
will  successively  appear  to  rise,  as  the  horizon  falls  below 
them,  while  those  near  W  will  successively  appear  to  set. 
It  is  obvious  that  the  observer  I  will  see  these  appearances 
earlier  than  a. 


CHAPTER  II. 

THE  RELATION  OF  THE   EARTH  TO  THE   HEAVENS— 

(Continued.) 

THE  CELESTIAL  SPHERE. 

Systems  of  Co-ordinates. — The  great  circles  of  the  celestial 
sphere  which  pass  through  the  two  celestial  poles  are  called 
hour-circles.  Each  hour-circle  is  the  celestial  meridian  of 
some  place  on  the  earth. 

The  hour-circle  of  any  particular  star  is  that  one  which 
passes  through  the  star  at  the  time.  As  the  earth  revolves, 
different  hour-circles,  or  celestial  meridians,  come  to  the 
star. 

In  Fig.  13  let  0  be  the  position  of  the  earth  in  the  centre  of 
the  celestial  sphere  NZ  SD.  Let  Zbe  the  zenith  of  the  ob- 
server at  a  given  instant,  and  P,  p,  the  celestial  poles.  By 
definition  P ZSpnNP  is  his  celestial  meridian.  (Each 
of  these  points  has  a  name;  let  the  student  give  the  names 
in  order.)  N S  is  the  horizon  of  the  observer  at  the  instant 
chosen.  PO  N  is  his  latitude.  If  P  is  the  north  pole,  he 
is  in  latitude  34°  north.  (See  page  31.) 

E  0  WD  is  the  celestial  equator;  E  and  W  are  the  east 
and  west  points.  The  earth  is  turning  from  W  to  E.  That 
is,  the  celestial  meridian  which  at  the  instant  chosen  in  the 
picture  contains  P  Zp  was  in  the  position  P  D  Rp  twelve 
hours  earlier. 


38  ASTRONOMY. 

PC,  PB9  PV,  PD  are  parts  of  hour-circles.  If  A  is 
a  star,  P  B  is  the  hour-circle  of  that  star.  As  the  earth 
turns  PB  turns  with  it,  and  directly  P  B  will  have  moved 
away  from  A  towards  the  top  of  the  picture  and  soon  P  V 
will  pass  through  the  star  A,  which  stands  still.  When  it 
does,  PV  will  be  the  hour-circle  of  A.  At  the  instant 
chosen  P  B  is  the  hour-circle  of  A.  The  stars  inside  the 
circle  NK  are  always  above  the  observer's  horizon.  Im  is 


FIG.  13. 


half  of  the  diurnal  orbit  of  one  of  the  north  stars.  All  the 
stars  inside  the  circle  SR  are  perpetually  invisible  to  the 
observer,  or  is  half  of  the  orbit  of  one  of  these  southern 
stars.  The  north-polar  distance  of  all  those  stars  perpetu- 
ally aboTe  the  horizon  is  less  than  or  equal  ioPN\  the 
south-polar  distance  of  all  the  stars  perpetually  invisible  is 
less  than  or  equal  to  p  S,  which  is  equal  to  P  N. 


RELATION  OP  THE  EARTH  TO  THE  HEAVENS.  39 

Altitude  and  Azimuth. — Z  G  is  the  vertical  circle  of  the 
star  A  at  the  instant  chosen  for  making  the  picture.  In 
a  few  moments  Z  will  have  moved  eastwards  and  a  new 
vertical  circle  will  have  to  be  drawn.  G  A  is  the  altitude 
of  A  at  the  instant;  in  a  few  moments  it  will  be  less.  For 
as  Z  moves  towards  the  eastward,  N  W S,  the  western  hori- 
zon of  the  observer,  will  move  upwards  (in  the  drawing) 
and  come  nearer  to  A,  which  stands  still.  Therefore  the 
altitude  of  A  will  diminish  progressively.  It  is  now  GA. 

The  azimuth  of  A  is  now  NG,  counted  from  the  north 
point.  It  will  change  as  Z  changes.  Having  the  altitude 
and  azimuth  of  A  at  the  instant,  the  observer  at  0  can  find 
it  in  the  sky.  (See  page  18.) 

North-Polar  Distance  and  Hour- Angle. — The  north-polar 
distance  of  A  is  PA.  This  will  serve  as  one  of  a  pair  of 
co-ordinates  to  point  out  the  apparent  position  of  A- in  the 
sky. 

The  hour-angle  of  a  star  is  the  angular  distance  between 
the  celestial  meridian  of  the  place  and  the  hour-circle  of 
that  star.  The  hour-angle  is  counted  from  the  meridian 
towards  the  west  from  0°  to  360°,  or  from  Oh  to  24h.  The 
hour-angle  of  A,  at  this  instant,  is  Z P  B.  The  hour- 
angle  of  a  star  K  is  0°. 

The  hour-angle  is  measured  by  the  arc  of  the  equator 
between  the  celestial  meridian  and  the  foot  of  the  hour- 
circle  through  the  star.  The  arc  C  B  measures  the  hour- 
angle  of  A  at  the  instant.  Directly,  Z  will  have  moved  away 
to  the  east  and  0  will  move  away  also  along  the  dotted  part 
of  the  line  representing  the  equator,  W  CUD. 

Having  the  two  co-ordinates  PA  and  C  B,  the  observer 
at"  0  can  find  the  star  A.  It  will  be  noticed  that  these  two 
co-ordinates,  polar  distance  and  hour-angle,  differ  in  one 


40  ASTRONOMT. 

respect  from  the  two  co-ordinates  altitude  and  azimuth. 
Both  the  latter  change  as  the  earth  revolves  on  its  axis.  Of 
the  former  only  one  changes;  viz.,  the  hour-angle.  The 
polar  distance  of  a  star  remains  the  same,  since  it  is  the  dis- 
tance from  a  fixed  point,  the  pole,  to  a  fixed  point,  the  star. 

Right  Ascension  and  North-Polar  Distance.— We  can 
devise  a  pair  of  co-ordinates  neither  of  which  shall  change 
as  the  earth  revolves.  This  will  clearly  be  convenient,  for 
this  pair  of  co-ordinates  will  be  the  same  for  every  observer 
and  for  every  hour  of  the  day,  whereas  the  others  vary  with 
the  time,  and  with  the  situation  of  the  observer. 

To  select  such  a  pair  we  have  simply  to  use  fixed  points 
in  the  celestial  sphere  to  count  from.  The  north  pole  will 
do  for  one  of  these,  and  the  north-polar  distance  of  the  star 
will  serve  for  one  co-ordinate.  This  is  measured,  for  the 
star  Ay  on  the  hour-circle  P B.  Let  us  choose  some  fixed 
point  V  on  the  equator  to  measure  our  other  co-ordinate 
from,  and  let  us  always  measure  it  on  the  equator  towards 
the  east  from  0°  to  360°  (from  Oh  to  24h).  That  is,  from 
V  through  B,  C,  Ey  D,  W,  successively. 

V B  is  the  right  ascension  of  A.  The  right  ascension  of 
a  star  is  the  angular  distance  of  the  foot  of  the  hour-circle 
through  the  star  from  the  vernal  equinox,  measured  on  tlte 
celestial  equator,  towards  the  east. 

Exactly  what  the  vernal  equinox  is  we  shall  find  out 
later  on;  for  the  present  it  is  sufficient  to  define  it  as  a 
certain  fixed  point  on  the  celestial  equator. 

If  we  have  the  right  ascension  and  north-polar  distance 
of  a  star,  we  can  point  it  out.  Thus  V B  and  PA  define 
the  position  of  A.  As  long  as  the  pole,  the  star,  and  the 
vernal  equinox  do  not  move  relatively  to  each  other  these 
two  co-ordinates  fix  the  position  of  the  star.  Their  relative 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.  41 

positions  are  not  affected  by  the  rotation  of  the  earth,  nor 
by  the  position  of  the  observer  upon  its  surface.  He  may 
be  in  any  latitude  or  any  longitude,  and  his  zenith  may  be 
anywhere  in,  the  whole  sky,  but  the  right  ascension  and 
the  north-polar  distance  of  each  star  remain  the  same  nev- 
ertheless. 

The  right  ascension  of  the  star  K  is  V  0.  Of  a  star  at  E 
it  is  V CE-,  of  a  star  at  D  it  is  VGED\  of  a  star  at  W 
it  is  V  C ED  W,  and  so  on. 

Right  Ascension  and  Decimation. — Sometimes  in  place 
of  the  north-polar  distance  of  a  star  it  is  convenient  to 
use  its  declination. 

The  declination  of  a  star  is  its  angular  distance  north  or 
south  of  the  celestial  equator. 

The  declination  of  A  is  BAy  which  is  90°  minus  PA. 

The  relation  between  N.  P.  D.  and  d  is 

N.  P.  D.  =  90°  -  tf;     d  =  90°  -  N.  P.  D. 

North  declinations  are  -J-;  South  declinations  are  — . 

The  declination  of  Z  is  C  Z.  CZ  is  equal  to  P  N,  since 
each  is  equal  to  90°  —  PZ.  PN  measures  the  latitude  of 
the  observer  whose  zenith  is  Z.  (See  page  31.) 

TJie  latitude  of  a  place  on  the  earth's  surface  is  measured 
ly  the  declination  of  its  zenith, 

This  is  the  definition  of  the  latitude  which  is  used  in 
astronomy. 

Co-ordinates  of  a  Star. — In  what  has  gone  before  we  have 
seen  that  there  are  various  ways  of  expressing  the  apparent 
positions  of  stars  on  the  surface  of  the  celestial  sphere. 
That  one  most  commonly  used  in  astronomy  is  to  give  the 
right  ascension  and  north-polar  distance  (or  declination)  of 
the  star.  The  apparent  position  of  the  star  is  fixed  by  these 


42  ASTRONOMY. 

two  co-ordinates.  If  we  know  its  distance  also,  the  abso- 
lute position  of  the  star  in  space  is  fixed  by  the  three  co- 
ordinates. Thus  we  have  a  complete  method  of  describing 
the  positions  of  the  heavenly  bodies. 

Co-ordinates  of  an  Observer. — To  describe  the  position  of 
an  observer  on  the  surface  of  the  earth  we  have  to  give  his 
latitude  and  longitude.  His  latitude  is  the  declination  of 
his  zenith;  his  longitude  is  the  fixed  angle  between  his 
celestial  meridian  and  the  celestial  meridian  of  Greenwich 
(or  Washington).  Declination  in  the  sky  is  analogous  to 
Latitude  on  the  earth.  Right  ascension  in  the  sky  is  anal- 
ogous to  Longitude  on  the  earth.  Both  of  these  co-ordi- 
nates depend  upon  the  position  of  his  zenith,  since  his 
longitude  is  nothing  but  the  angular  distance  of  his  zenith 
west  of  the  zenith  of  Greenwich. 

All  this  is  extremely  simple,  but  if  it  is  clearly  under- 
stood the  student  has  it  in  his  power  to  answer  a  great 
many  interesting  questions  for  himself. 

We  know,  for  example,  that  the  sun  is  in  the  equator  and  at  the 
vernal  equinox  on  March  21st  of  each  year. 

The  student  can  determine  for  himself  what  appearances  will  be 
presented  on  that  day  next  year.  He  may  proceed  in  this  way:  Draw 
a  circle  to  represent  the  celestial  sphere.  Take  a  point,  P,  of  it  to 
be  the  position  of  the  north  pole  in  the  sky.  If  the  observer  lives 
in  a  place  whose  latitude  is  <p  degrees  north,  his  zenith  will  be 
90°  —  <p  from  the  north  pole  measured  towards  the  south.  Measure 
off  9(T  —  q>  on  the  circle  from  P.  The  end  of  that  arc  is  the  zenith 
of  that  observer,  Z.  PZ  is  an  arc  of  his  celestial  meridian.  Meas- 
ure from  P  through  Z  90°,  and  the  end  of  that  arc  is  on  the  equator, 
Q  say.  Join  P  with  the  centre,  0,  of  the  circle.  This  line  is  the 
direction  of  the  celestial  pole.  Join  0  and  Q,  and  this  line  (perpen- 
dicular to  P  0)  is  the  direction  of  that  point  of  the  equator  which  is 
highest  above  his  horizon.  Draw  the  liueZO;  this  is  the  vertical 
line.  Through  0  draw NOS  perpendicular  to  Z  0.  This  is  the  north 
and  south  line  of  his  horizon.  Draw  the  ovals  which  represent  (in 


RELATION  Of  THE  EARTH  TO  THM  HEAVENS.  43 

perspective)  the  circles  of  the  equator  and  of  the  horizon.  Assume 
a  point,  V,  of  the  celestial  equator.  On  March  21st  of  each  year  the 
sun  is  there.  When  the  sun  is  at  the  highest  point  Q  of  the  equatoi 
it  is  noon  to  this  observer.  The  sun  is  on  his  meridian.  Six  hours 
before  this  time  the  sun  will  rise  to  him;  six  hours  after  he  will 
set.  It  requires  twenty-four  hours  for  the  point  Fto  be  apparently 
carried  all  round  the  equator,  and  the  sun  appears  to  go  with  the 
point.  Three  months  later  the  sun  is  about  90°  of  right  ascension 
and  has  a  north  polar  distance  of  66|°.  The  student  can  determine 
in  the  same  way  the  circumstances  under  which  the  sun  will  appear 
to  him  to  move  on  the  21st  of  next  June  when  its  north-polar  distance 
is  664°,  or  on  December  21st,  when  its  K  P.  D.  is  113f. 

The  example  that  is  here  given  is  not  for  the  purpose  of  teaching 
the  student  what  the  motion  of  the  sun  is;  that  will  be  considered  in 
its  proper  order  in  this  book.  But  it  is  to  show  him  that  if  he  wishes 
to  know  about  it  he  can  find  out  for  himself. 

When  he  reads  about  the  midnight  sun  that  is  visible  in  the  Arctic 
regions  he  can  verify  the  facts  for  himself.  Let  him  construct  the 
diagram  we  have  described  for  a  place  whose  latitude  is  80°  north 
and  see  what  sort  of  a  diurnal  orbit  the  sun  will  describe  on  the  21st 
of  June  when  its  N.  P.  D.  is  66^°. 


RELATION  OF  TIME  TO  THE  SPHEEE. 

Sidereal  Time.  —  The  earth  rotates  uniformly  on  its  axis; 
that  is,  it  turns  through  equal  angles  in  equal  intervals  of 
time. 

This  rotation  can  be  used  to  measure  any  intervals  of 
time  when  once  a  unit  of  time  is  agreed  upon.  The  most 
natural  and  convenient  unit  is  a  day.  There  are  various 
kinds  of  days,  and  we  have  to  take  them  as  they  are. 

A  sidereal  day  is  the  interval  of  time  required  for  the 
earth  to  rotate  once  on  its  axis.  Or  what  is  the  same  thing, 
it  is  the  interval  of  time  between  two  consecutive  tran- 
sits of  any  star  over  the  same  celestial  meridian.  The 
sidereal  day  is  divided  into  24  sidereal  hours;  each  hour  is 
divided  into  60  minutes;  each  minute  into  60  seconds.  In 
making  one  revolution  the  earth  turns  through  360°,  so  that 


44  ASTRONOMY. 

24  hours  =  360°;  also, 

1  hour  =  15°;  1°  =  4  minutes. 
1  minute  =  15';  1'  =  4  seconds. 
1  second  =  15*;  1'  =  0.066  second. 

When  a  star  is  on  the  celestial  meridian  of  any  place  its 
hour-angle  is  zero,  by  definition  (see  page  39).  It  is  then 
at  its  transit  or  culmination. 

As  the  earth  rotates,  the  meridian  moves  away  (east- 
wardly)  from  this  star,  whose  hour-angle  continually  in- 
creases from  0°  to  360°,  or  from  0  hours  to  24  hours. 
Sidereal  time  can  then  be  directly  measured  by  the  hour- 
angle  of  any  star  in  the  heavens  which  is  on  the  meridian 
at  an  instant  we  agree  to  call  sidereal  0  hours.  When  this 
star  has  an  hour-angle  of  90°,  the  sidereal  time  is  6  hours; 
when  the  star  has  an  hour  angle  of  180°  (and  is  again  on 
the  meridian,  but  invisible  unless  it  is  a  circumpolar  star),  it 
is  12  hours ;  when  its  hour-angle  is  270°,  the  sidereal  time 
is  18  hours;  and,  finally,  when  the  star  reaches  the  upper 
meridian  again,  it  is  24  hours  or  0  hours.  (See  Fig.  13, 
where  E  C  WD  is  the  apparent  diurnal  path  of  a  star  in 
the  equator.  It  is  on  the  meridian  at  C.) 

Instead  of  choosing  a  star  as  the  determining  point 
whose  transit  marks  sidereal  0  hours,  it  is  found  more  con- 
venient to  select  that  point  in  the  sky  from  which  the  right 
ascensions  of  stars  are  counted — the  vernal  equinox — the 
point  V  in  the  figure.  The  fundamental  theorem  of  si- 
dereal time  is:  The  hour-angle  of  tie  vernal  equinox,  or  the 
sidereal  time,  is  equal  to  the  right  ascension  of  the  meri- 
dian; that  is,  C  V=  VO. 

To  avoid  continual  reference  to  the  stars,  we  set  a  clock 
so  that  its  hands  shall  mark  0  hours  0  minutes  0  seconds 


RELATION  OF  THE  fiAllTII  TO   THE  HEAVENS.  45 

at  the  transit  of  the  vernal  equinox,  and  regulate  it  so  that 
its  hour-hand  revolves  once  in  24  sidereal  hours.  Such  a 
clock  is  called  a  sidereal  clock. 

Solar  Time. — Time  measured  by  the  hour-angle  of  the 
sun  is 'called  true  or  apparent  solar  time.  An  apparent 
solar  day  is  the  interval  of  time  between  two  consecutive 
transits  of  the  sun  over  the  upper  meridian.  The  instaut 
of  the -transit  of  the  sun.  over  the  meridian  of  anyplace 
is  the  apparent  noon  of  that  place,  or  local  apparent  noon. 

When  the  sun's  hour-angle  is  12  hours  or  180°,  it  is 
local  apparent  midnight. 

The  ordinary  sun-dial  marks  apparent  solar  time.  As 
a  matter  of  fact,  apparent  solar  days  are  not  equal.  The 
reason  for  this  will  be  fully  explained  later.  Hence  our 
clocks  are  not  made  to  keep  this  kind  of  time,  for  if  once 
set  right  they  would  sometimes  lose  and  sometimes  gain 
on  such  time. 

Mean  Solar  Time. — A  modified  kind  of  solar  time  is 
therefore  used,  called  mean  solar  time.  This  is  the  time 
kept  by  ordinary  watches  and  clocks.  It  is  sometimes 
called  civil  time.  Mean  solar  time  is  measured  by  the  hour- 
angle  of  the  mean  sun,  a  fictitious  body  which  is  imagined 
to  move  uniformly  in  the  equator.  The  law  according  to 
which  the  mean  sun  is  supposed  to  move  enables  us  to  com- 
pute its  exact  position  in  the  heavens  at  any  instant,  and  to 
define  this  position  by  the  two  co-ordinates  right  ascension 
and  declination.  Thus  we  know  the  position  of  this  imagi- 
nary body  just  as  we  know  the  position  of  a  star  whose 
co-ordinates  are  given,  and  we  may  speak  of  its  transit  as 
if  it  were  a  bright  material  point  in  the  sky.  A  mean 
solar  day  is  the  interval  of  time  between  two  consecutive 
transits  of  the  mean  sun  over  the  upper  meridian.  Mean 


46  ASTRONOMY. 

noon  at  any  place  on  the  earth  is  the  instant  of  the  mean 
sun's  transit  over  the  meridian  of  that  place.  Twelve  hours 
after  local  mean  noon  is  local  mean  midnight.  The  mean 
solar  day  is  divided  into  24  hours  of  60  minutes  each.  Each 
minute  of  mean  time  contains  60  mean  solar  seconds. 
Astronomers  begin  ^the  mean  solar  day  at  noon,  which  is  0 
hours,  and  count  round  to  24  hours. 

"We  have  thus  three  kinds  of  time.  They  are  alike  in  one  point: 
each  is  measured  by  the  hour-angle  of  some  body,  real  or  assumed. 
The  body  chosen  determines  the  kind  of  time,  and  the  absolute  length 
of  the  unit — the  day.  The  simplest  unit  is  that  determined  by  the 
uniformly  rotating  earth — the  sidereal  day;  the  most  natural  unit  is 
that  determined  by  the  sun  itself — the  apparent  solar  day,  which, 
however,  is  a  variable  unit;  the  most  convenient  unit  is  the  mean 
solar  day,  and  this  is  the  one  chosen  for  use  in  our  daily  life. 

Comparative  Lengths  of  the  Mean  Solar  and  Sidereal 
Day. — As  a  fact  of  observation,  it  is  found  that  the  sun 
appears  to  move  from  west  to  east  among  the  stars,  about 
1°  daily,  making  a  complete  revolution  around  the  sphere 
in  a  year.  It  requires  365£  days  to  move  through  360°. 

Hence  an  apparent  solar  day  will  be  longer  than  a  side- 
real day.  For  suppose  the  sun  to  be  at  the  vernal  equinox 
exactly  at  sidereal  noon  (0  hours)  of  Washington  time  on 
March  21st;  that  is,  the  vernal  equinox  and  the  sun  are 
both  on  the  meridian  of  Washington  at  the  same  instant. 
In  24  sidereal  hours  the  vernal  equinox  will  again  be  on  the 
same  meridian,  but  the  sun  will  have  moved  eastwardly  by 
about  a  degree,  and  the  earth  will  have  to  turn  through 
this  angle  and  a  little  more  in  order  that  the  sun  shall 
again  be  on  the  Washington  meridian,  or  in  order  that  it 
may  be  apparent  noon  on  March  22d.  For  the  meridian 
to  overtake  the  sun  requires  about  4  minutes  of  ^sidereal 


RELATION  OF  THE  EARTH  TO   THE  HEAVENS.   47 

time.  The  true  sun  does  not  move,  as  we  have  said,  uni- 
formly. The  mean  sun  is  supposed  to  move  uniformly, 
and  to  make  the  circuit  of  the  heavens  in  the  same  time  as 
the  real  sun.  Hence  a  mean  solar  day  will  also  be  longer 
than  a  sidereal  day,  for  the  same  reason  that  the  apparent 
solar  day  is  longer.  The  exact  relation  is: 

1  sidereal  day  =  0^997  mean  solar  day, 

24  sidereal  hours  =  23h  56m  4s -091  mean  solar  time, 

1  mean  solar  day  =  1-003  sidereal  days, 

24  mean  solar  hours  =  24h  3m  56s -555  sidereal  time, 

and 

366-24222  sidereal  days  =  365-24222  mean  solar  days. 

Local  Time. — When  the  mean  sun  is  on  the  meridian  of 
a  place,  as  Boston,  it  is  mean  noon  at  Boston.  When  the 
mean  sun  is  on  the  meridian  of  St.  Louis,  it  is  mean  noon 
at  St.  Louis.  St.  Louis  being  west  of  Boston,  and  the 
earth  rotating  from  west  to  east,  the  local  noon  of  Boston 
occurs  before  the  local  noon  at  St.  Louis.  In  the  same 
way  the  local  sidereal  time  at  Boston  at  any  given  instant 
is  expressed  by  a  larger  number  than  the  local  sidereal  time 
of  St.  Louis  at  that  instant. 

The  sidereal  time  of  mean  noon  is  given  in  the  astro- 
nomical ephemeris  for  every  day  of  the  year.  It  can  be 
found  within  ten  or  twelve  minutes  at  any  time  by  remem- 
bering that  on  March  21st  it  is  sidereal  0  hours  about 
noon,  on  April  21st  it  is  about  two  hours  sidereal  time  at 
noon,  and  so  on  through  the  year.  Thus,  by  adding  two 
hours  for  each  month,  and  four  minutes  for  each  day  after 
the  21st  day  last  preceding,  we  have  the  sidereal  time  at 
the  noon  we  require.  Adding  to  it  the  number  of  hours 
since  noon,  and,  one  minute  more  for  every  fourth  of  a  day 


48  ASTRONOMY. 

on  account  of  the  constant  gain  of  the  clock  (4m  daily),  we 
have  the  sidereal  time  at  any  moment, 

Example.—  Find  the  sidereal  time  on  July  4th,  1381,  at  4  o'clock 
A.M.  We  have: 

h      m 

June  21st,  3  mouths  after  March  21st;  to  be  X  2,  60 

July  3d,  12  days  after  June  21st;  X  4,  0  48 

4  A.M.,  16  hours  after  noon,  nearly  f  of  a  day,  16    3 

22  51 
This  result  is  within  a  miuute  of  the  exact  value. 

Relation  of  Time  and  Longitude. — Considering  our  civil 
time  which  depends  on  the  sun,  it  will  be  seen  that  it  is 
noon  at  any  and  every  place  on  the  earth  when  the  sun 
crosses  the  meridian  of  that  place,  or,  to  speak  with  more 
precision,  when  the  meridian  of  the  place  passes  under  the 
sun.  In  the  lapse  of  24  hours  the  rotation  of  the  earth  on 
its  axis  brings  all  its  meridians  under  the  sun  in  succession, 
or,  which  is  the  same  thing,  the  sun  appears  to  pass  in  suc- 
cession over  all  the  meridians  of  the  earth.  Hence  noon 
continually  travels  westward  at  the  rate  of  15°  in  an  hour, 
making  the  circuit  of  the  earth  in  24  hours.  The  differ- 
ence between  the  time  of  day,  or  the  Inntl  lime  as  it  is  called, 
at  any  two  places  will  be  in  proportion  to  their  difference 
of  longitude,  amounting  to  one  hour  for  every  15  degrees  of 
longitude,  four  minutes  for  every  degree,  and  so  on.  Vice 
versa,  if  at  the  same  real  moment  of  time  we  can  determine 
the  local  times  at  two  different  places,*  the  difference  of  these 
times  multiplied  by  15  will  give  the  difference  of  longitude. 

The  longitudes  of  places  are  determined  astronomically 
on  this  principle.  Astronomers  are,  however,  in  the  habit 
of  expressing  the  longitude  of  places  on  the  earth  like  the 

*  And  compare  the  two,  by  telegraph  for  example. 


RELATION  OF  THE  xmRTH  TO  THE  HEAVEN 8.  49 

right  ascensions  of  the  heavenly  bodies,  not  in  degrees,  but 
in  hours.  For  instance,  instead  of  saying  that  Washington 
is  77°  3'  west  of  Greenwich,  we  commonly  say  that  it  is  5 
hours  8  minutes  12  seconds  west,  meaning  that  when  it  is 
noon  at  Washington  it  is  5  hours  8  minutes  12  seconds 
after  noon  at  Greenwich.  This  course  is  adopted  to  prevent 
the  trouble  and  confusion  which  might  arise  from  constantly 
having  to  change  hours  into  degrees  and  the  reverse. 

Where  does  the  Day  Change?— A  question  frequently 
asked  in  this  connection  is,  Where  does  the  day  change? 
It  is,  we  will  suppose,  Sunday  noon  at  Washington.  That 
noon  travels  all  the  wny  round  the  earth,  and  when  it  gets 
back  to  Washington  again  it  is  Monday.  Where  or  when 
did  it  change  from  Sunday  to  Monday  ?  We  answer, 
wherever  people  choose  to  make  the  change.  Navigators 
make  the  change  occur  in  longitude  180°  from  Greenwich. 
As  this  meridian  lies  in  the  Pacific  Ocean,  and  meets 
scarcely  any  land  through  its  course,  it  is  very  convenient  for 
this  purpose.  If  its  use  wore  universal,  the  day  in  question 
would  be  Sunday  to  all  the  inhabitants  east  of  this  line,  and 
Monday  to  every  one  west  of  it.  But  in  practice  there  have 
been  some  deviations.  As  a  general  rule,  on  those  islands 
of  the  Pacific  which  were  settled  by  men  travelling  east  the 
day  would  at  first  be  called  Monday,  even  though  they 
might  cross  the  meridian  of  180°.  Indeed  the  Russian 
settlers  carried  their  count  into  Alaska,  so  that  when  our 
people  took  possession  of  that  territory  they  found  that 
the  inhabitants  called  the  day  Monday  when  they  them- 
selves called  it  Sunday.  These  deviations  have,  however, 
almost  entirely  disappeared,  and  with  few  exceptions  the 
day  is  changed  by  common  consent  in  longitude  180°  from 
Greenwich, 


50  ASTRONOMY. 

DETERMINATIONS  OF  TEBRESTBIAL   LONGITUDES 

Owing  to  the  rotation  of  the  earth,  there  is  no  such  fixed 
correspondence  between  meridians  on  the  earth  and  among 
the  stars  as  there  is  between  latitude  on  the  earth  and  de- 
clination in  the  heavens.  The  observer  can  always  deter- 
mine his  latitude  by  finding  the  declination  of  his  zenith, 
but  he  cannot  find  his  longitude  from  the  right  ascension 
of  his  zenith  with  the  sumo  facility,  because  that  right  as- 
cension  is  constantly  changing.  To  determine  the  longi- 
tude of  a  place,  the  element  of  time  as  measured  by  the 
diurnal  motion  of  the  earth  necessarily  comes  in.  Con- 
sider the  plane  of  the  meridian  of  a  place  extended  out  to 
the  celestial  sphere  so  as  to  mark  out  on  the  latter  the 
celestial  meridian  of  the  place.  Take  two  such  places, 
Washington  and  San  Francisco  for  example ;  then  there 
will  be  two  such  celestial  meridians  cutting  the  celes- 
tial sphere  so  as  to  make  an  angle  of  about  forty-five  de- 
grees with  each  other  in  this  case.  Let  the  observer  imagine 
himself  at  San  Francisco.  Then  he  may  conceive  the 
meridian  of  Washington  to  be  visible  on  the  celestial  sphere, 
and  to  extend  from  the  pole  over  toward  his  south-east 
horizon  so  as  to  pass  at  a  distance  of  about  forty-five  degrees 
east  of  his  own  meridian.  It  would  appear  to  him  to  be  at 
rest,  although  really  both  his  own  meridian  and  that  of 
Washington  are  moving  in  consequence  of  the  earth's  rota- 
tion. Apparently  the  stars  in  their  course  will  first  pass 
the  meridian  of  Washington,  and  about  three  hours  later 
will  pass  his  own  meridian.  Now  it  is  evident  that  if  he 
can  determine  the  interval  which  the  star  requires  to  pass 
from  the  meridian  of  Washington  to  that  of  his  own  place, 
he  will  at  once  have  the  difference  of  longitude  of  the  two 


RELATION  OF  THE  EAETH  TO  THE  HEAVENS.  51 

places  by  simply  turning  the  interval  in  time  into  degrees 
at  the  rate  of  fifteen  degrees  to  each  hour. 


FIG.  14. 

The  difference  of  longitude  between  any  two  places  de- 
pends upon  the  angular  distance  of  the  terrestrial  (or  celes- 
tial) meridians  of  these  two  places  and  not  upon  the  motion 
of  the  star  or  sun  which  is  used  to  determine  this  angular 
difference,  and  hence  the  longitude  of  a  place  is  the  same 
whether  expressed  as  the  difference  of  two  sidereal  or  of 
two  solar  times.  The  longitude  of  Washington  west  from 
Greenwich  is  5h  8m  or  77°,  and  this  is  in  fact  the  ratio  of 
the  angular  distance  of  the  meridian  of  Washington  from 
that  of  Greenwich,  to  24  hours  or  360°.  The  angle  between 
the  two  meridians  is  -gfo  of  24  hours,  or  of  a  whole  circum- 
ference. 


52  ASTRONOMY. 

It  is  thus  plain  that  the  difference  of  longitude  of  any  tivo 
places  is  the  same  as  the  difference  of  their  simultaneous 
local  times  ;  and  this  whether  the  local  times  spoken  of 
are  both  sidereal  or  both  solar. 

METHODS  OF  DETERMINING  THE  DIFFERENCE  OF  LONGI- 
TUDE OF  Two  PLACES  ON  THE  EARTH. 

Every  purely  astronomical  method  depends  upon  the 
principle  we  have  just  laid  down. 

It  is  of  vital  importance  to  seamen  to  be  able  to  deter- 
mine the  longitude  of  their  vessels.  The  voyage  from  Liv- 
erpool to  New  York  is  made  weekly  by  scores  of  steamers, 
and  the  safety  of  the  voyage  depends  upon  the  certainty 
with  which  the  captain  can  mark  the  longitude  and  lati- 
tude of  his  vessel  upon  the  chart. 

The  method  used  by  a  sailor  is  this  :  with  a  sextant  (see 
Chapter  III.)  the  local  time  of  the  ship's  position  is  deter- 
mined by  an  observation  of  the  sun.  That  is,  on  a  given 
day  he  can  set  his  watch  so  that  its  hands  point  to  twelve 
hours  when  the  sun  is  on  his  meridian  on  that  day.  He 
carries  a  chronometer  (which  is  merely  a  very  fine  watch) 
whose  hands  point  always  to  Greenwich  time.  Suppose 
that  when  the  ship's  time  is  Oh  or  noon  the  Greenwich 
time  is  3h  20m.  Evidently  he  is  west  of  Greenwich  3h  20ra, 
since  that  is  the  difference  of  the  simultaneous  local  times, 

and  since  the  Greenwich  time  is  later.     Hence  he  is  some- 

• 

where  on  the  meridian  of  50°  west.  If  he  has  determined 
the  altitude  of  the  pole  or  the  declination  of  his  zenith  in 
any  way,  then  he  has  his  latitude  also.  If  this  should  be 
45°  north,  the  ship  is  in  the  regular  track  between  New 
York  and  Liverpool,  and  he  can  go  on  with  safety. 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.  53 

When  the  steamer  Faraday  was  laying  the  direct  cable  she  got  her 
longitude  every  day  by  comparing  her  ship's  time  (found  by  obser- 
vation on  board)  with  the  Greenwich  time  telegraphed  along  the  cable 
and  received  at  the  end  of  it  which  she  had  on  her  deck.  Longitudes 
may  be  determined  in  the  same  way  on  shore. 

From  an  observatory,  as  Washington,  the  beats  of  a  clock  are  sent 
out  by  telegraph  along  the  lines  of  railway;  at  every  railway  station 
and  telegraph  office  the  telegraph  sounder  beats  the  seconds  of  the 
Washington  clock.  Any  one  who  can  set  his  watch  to  the  local  time 
of  his  station  and  who  can  compare  it  with  the  signals  of  the  Wash- 
ington clock  (which  are  sent  at  Washington  noon,  daily  except  Sun. 
day)  can  determine  for  himself  the  difference  of  the  simultaneous 
local  times  of  Washington  and  of  his  station,  and  thus  his  own  longi- 
tude east  or  west  from  Washington. 


METHODS  OF  DETERMINING  THE  LATITUDE  OF  A  PLACE 
ON  THE  EARTH. 

Latitude  from   Circumpolar  Stars. — In  the  figure  sup- 
pose Z to  be  the  zenith  of  the  observer,  H ZRN  his  me- 


90°  -  cp  =  p  -f  z', 
90°  -  <p  =  z"  -p, 
90°  -  <p  =  \(z'  +  z"); 
p  =  i(z"  -  z'). 


Fia.  15. 


ridian,  P  the  north  pole,  H R  his  horizon.  Suppose  Sand. 
S'  to  be  the  two  points  where  a  circumpolar  star  crosses 
the  meridian,  as  it  moves  around  the  pole  in  its  apparent 


54 


ASTRONOMY. 


diurnal  orbit.     P  8  =  P  S'  is  the  star's  north-polar  dis- 
tance, and  P  H  =  (p  =  the  observer's  latitude. 

ZS+ZS' 


Therefore 


<p  =  90°  - 


=  ZP  =  90°  -  (p. 
ZS+ZS' 


We  can  measure  Z  S  and  Z  S',  the  zenith  distances  of  the 
star  in  the  two  positions,  by  the  meridian  circle  or  by  the 
sextant,  as  will  be  explained  in  the  next  chapter.  Hence 
having  these  zenith  distances  we  have  the  latitude  of  the 
place. 

Latitude  by  the  Meridian  Altitude  of  the  Sun  or  a  Star. 
—  In  the  figure  let  Z  be  the  observer's  zenith,  P  the  pole, 

and  Q  the  intersection  of 
the  celestial  equator  with  the 
meridian  H  Z  H.  The  alti- 
tude of  the  star  S  is  meas- 
ured when  the  star  is  on  the 
meridian.  It  is  known  to 
be  on  the  meridian  when  we 
find  its  altitude  to  be  a  max- 
Fl0-16-  imum.  From  the  measured 

altitude  of  the  star  S  we  deduce  its  zenith  distance  Z  S  =  2 
=  90°  —  HS.  Its  declination  is  taken  from  a  catalogue  of 
stars  if  it  is  a  star,  or  from  the  Nautical  Almanac  if  it  is 
the  sun.  In  either  case  the  declination  Q  S  is  known. 

ZQ  =  QS  +  ZS-, 


If  the  body  culminates  north  of  the  zenith  at  /S", 
ZQ=QS'-ZS'i 
<z=    6     -2. 


vT 

RELATION  OF  THE  EARTH  TO   THE  HEAVENS.   55 

This  is  the  method  uniformly  employed  at  sea,  where  the 
altitude  of  the  sun  at  apparent  noon  is  daily  measured. 


PARALLAXES  AND  SEMIDIAMETERS  OF  THE  HEAVENLY 
BODIES. 

The  apparent  position  of  a  body  on  the  celestial  sphere 
remains  the  same  as  long  as  the  observer  is  fixed,  as  has 
been  shown  (see  page  20).  If  the  observer  changes  his 
place  and  the  star  remains  in  the  same  position,  the  ap- 


Fio.  17. 

parent  position  of  the  star  will  change.  To  show  this  let 
CH'  be  the  earth,  C  being  its  centre.  8'  and  S"  are  the 
places  of  two  observers  on  the  surface.  Z'  and  Z"  are 
their  zeniths  in  the  celestial  sphere  H' P" .  P  is  a  star. 
S'  will  see  P  in  the  apparent  position  Pf.  S"  will  see  P 
in  the  apparent  position  P".  That  is,  two  different  ob- 
servers see  the  same  object  in  two  different  apparent 
positions.  If  the  observer  8'  moves  along  the  surface 
directly  to  S",  the  apparent  position  of  P  on  the  celes- 
tial sphere  will  appear  to  move  from  P'  to  P". 
This  change  is  due  to  the  parallax  of  P. 


56  ASTRONOMY. 

The  parallax  of  a  body  due  to  a  change  in  the  position 
of  the  observer,  is  the  alteration  in  the  apparent  position 
of  the  body  caused  by  that  change. 

If  the  observer  at  S'  could  move  to  the  centre  of  the 
earth  along  the  line  S'C9  the  apparent  position  of  P  would 
move  from  P*  to  Pt.  If  the  observer  at  S"  could  move 
from  S*  to  C  along  S'C,  the  apparent  position  of  P  would 
move  from  P"  to  Pt. 

In  the  triangle  P  S'C  the  following  parts  are  known: 

C  P  =  A  =  the  geocentric  distance  of  P, 
C  S'  =  p'  =•  the  radius  of  the  earth  at  S', 

and  the  angle  S'PC=  P'PP,  is  \\\cparallax  of  P. 

For  the  change  of  apparent  position  of  P  from  P'  to  P t 
is  due  to  the  change  of  the  point  of  observation  from  S'  to 
C. 

Similarly  the  angle  S'PC  =  P"PPt  is  the  parallax  of  P 
relative  to  a  change  of  the  observer  fiom  S"  to  C. 

Horizontal  Parallax. — Clearly  the  parallax  of  P  differs 
for  observers  differently  situated  on  the  earth,  and  it  is 
necessary  to  take  some  standard  parallax  for  each  observer. 
Such  a  standard  is  the  horizontal  parallax.  Suppose  P 
to  be  in  the  horizon  of  the  observer  £';  then  Z'S'P 
will  be  90°,  as  will  also  the  angle  PS'C.  In  the  triangle 
S'PC  three  parts  "will  then  be  known  and  the  horizontal 
parallax  (the  angle  at  P  when  P  is  in  the  horizon)  can  be 
found.  It  will  be  the  same  for  the  observer  at  S".  When 
P  is  in  the  horizon  of  S",  Z"S"P  is  a  right  angle,  as  is  also 
PS"C.  C  P  and  C  S'  are  known  and  thus  the  horizontal 
parallax  of  P  is  determined. 

If  CP,  the  distance  of  P,  increases,  other  things  remain- 
ing the  same,  the  parallax  of  P  will  diminish. 


DELATION  OF  THE  EARTH  TO  THE  HEAVENS.  57 

The  student  can  prove  this  for  himself  by  drawing  the 
figure  on  the  same  scale  as  here  given,  making  GP  larger. 

The  angles  at  P  (the  parallaxes)  will  become  smaller  and 
smaller  the  larger  GP  is  taken.  Hence  the  magnitude  of 
the  parallax  of  a  star  or  a  planet  depends  upon  its  distance 
from  us. 

Suppose  an  observer  at  the  point  P  looking  at  the  earth's 
radius  S'C.  The  angle  subtended  by  that  semidiameter 
is  the  same  as  the  parallax  of  P.  Hence  we  may  say  that 
the  parallax  of  a  body  with  reference  to  an  observer  on  the 
earth  is  measured  by  the  angle  subtended  at  the  body  by 
that  semidiameter  of  the  earth  which  passes  through  the 
observer's  station. 

As  the  point  P  is  carried  further  and  further  away  from 
the  earth,  the  angle  subtended  by  Sf  C,  for  example,  becomes 
less  and  less.  If  P  were  at  the  distance  of  the  moon,  this 
angle  would  be  about  57';  if  at  the  distance  of  the  sun, 
it  would  be  about  8-J".  S'C  is  roughly  4000  miles;  it 
subtends  an  angle  of  57'  at  the  distance  of  the  moon.  70 
miles  would  subtend  an  angle  of  about  1',  and  3437' 
would  be  about  240,000  miles.  This  is  the  distance  of  the 
moon  from  the  earth.  (See  pages  4,  5.) 

Again,  4000  miles  subtends  an  angle  of  8*.  5  at  the  dis- 
tance of  the  sun.  470. 7  miles  would  subtend  an  angle  of 
I",  and  206,264". 8  would  be  97,000,000  miles,  and  this  is 
about  the  distance  of  the  sun.  By  taking  the  exact  values 
of  the  radius  of  the  earth  and  of  the  solar  parallax,  this  dis- 
tance is  found  to  be  about  93,000,000  miles. 

The  example  shows  the  method  of  calculating  the  sun's 
distance  when  we  have  two  things  accurately  given:  first, 
the  dimensions  of  the  earth;  and  second,  the  parallax  e£ 
the  sun. 


58  ASTRONOMY 

Annual  Parallax. — "We  have  seen  that  for  the  moon  the 
parallax  is  about  1°;  for  the  sun  it  is  only  8*;  for  some  of 
the  more  distant  planets  it  is  considerably  less. 

For  Jupiter  it  is  about  2*;  for  Saturn  less  than  1*;  for 
Neptune  about  0*.3. 

Let  us  remember  what  this  means.  It  means  that  4000 
miles,  the  earth's  radius,  would  subtend  at  the  distance  of 
Neptune  an  angle  of  only  ^  of  a  single  second  of  arc. 

The  parallax  of  the  moon  is  determined  by  observation, 
and  the  observation  consists  in  measuring  the  angle  which 
the  radius  of  the  earth  ivould  subtend  if  viewed  from  the 
moon's  centre.  57'  is  an  angle  large  enough  to  be  deter- 
mined quite  accurately  in  this  way.  There  would  be  but  a 
small  per  cent  of  error.  Even  S",  the  sun's  parallax,  can  be 
measured  so  as  to  have  an  error  of  not  more  than  2  or  3 
per  cent. 

But  this  method  will  not  do  to  measure  anything  much 
smaller  than  8".  The  parallax  of  a  fixed  star,  for  example, 
is  not  sTnsWir  Par^  °*  large  as  the  sun's  parallax:  and  this 
is  too  minute  a  quantity  to  be  deduced  by  these  methods. 
We  therefore  use  for  distant  bodies  a  parallax  which  does 
not  depend  on  the  radius  of  the  earth,  but  upon  the  radius 
of  the  earth's  orbit  around  the  sun. 

Tlie  annual  parallax  of  a  body  is  the  angle  subtended  at 
the  body  by  the  radius  of  the  earth's  orbit  seen  at  right 
angles. 

For  example,  in  Fig.  18  suppose  that  C  now  represents 
the  fiun,  around  which  the  earth  S'  moves  in  the  nearly 
circular  orbit  S'S"H'.  S'Cis  no  longer  4000  miles  as  in 
the  last  example,  but  it  is  93,000,000  miles.  Suppose  P  to 
be,  again,  a  body  whose  annual  parallax  is  S'P  G  (suppos- 
ing PS'Cto  be  a  right  angle). 


RELATION  OF  THE  EAHTH  TO  THE  HEAVENS.  59 

Some  of  the  nearest  fixed  stars  have  an  annual  parallax 
of  nearly  If.  Hence  the  nearest  of  them  are  not  nearer 
than  206,2^4  times  93,000,000  miles.  The  greater  number 
of  them  have  a  parallax  of  not  more  than  -fa". 

Hence  their  distances  cannot  be  less  than 

10  X  206,264  X  93,000,000  miles. 

To  the  student  who  has  understood  the  simple  rules  given 
on  pages  4  and  5  these  deductions  will  be  plain. 


FIG.  18. 

Semidiameters  of  the  Heavenly  Bodies. — The  angular 
semidiameter  of  the  sun  as  seen  from  the  earth  is  961ff. 
Hence  its  diameter  is  1922".  Its  real  diameter  in  miles  is 
therefore  about  880,000,  as  its  distance  is  93,000,000  miles. 

The  angular  semidiameter  of  the  moon  as  seen  from  the 
earth  is  about  15^'.  Hence  its  real  diameter  is  about  2000 
miles,  its  distance  being  about  240,000  miles. 

In  the  same  way,  knowing  the  distance  of  any  planet  and 
measuring  its  angular  semidiameter,  we  can  compute  its 
dimensions  in  miles. 


CHAPTER  III. 

ASTRONOMICAL  INSTRUMENTS. 

General  Account. — In  a  general  way  we  may  divide  the 
instruments  of  astronomy  into  two  classes,  seeing  instru- 
ments and  measuring  instruments. 

The  seeing  instruments  are  telescopes ;  they  have  for 
their  object  either  to  enable  the  observer  to  see  faint  objects 
as  comets  or  small  stars,  or  to  enable  him  to  see  brighter 
stars  with  greater  precision  than  he  could  otherwise  do. 
How  they  accomplish  this  we  shall  shortly  explain.  The 
measuring  instruments  are  of  two  classes.  The  first  class 
measures  intervals  of  time.  The  second  measures  angles. 
A  clock  is  a  familiar  example  of  the  first  class;  a  divided 
circle  of  the  second. 

Let  us  take  these  in  the  order  named. 

The  Refracting  Telescope. — The  refracting  telescope  is 
composed  of  two  essential  parts,  the  object-glass  or  objec- 
tive and  the  eye-piece. 

The  object-glass  is  for  the  sole  purpose  of  collecting  the 
rays  of  light  which  emanate  from  the  thing  looked  at,  and 
for  making  an  image  of  this  thing  at  a  point  which  is  called 
the  focus  of  the  objective. 

The  eye-piece  has  for  its  sole  object  to  magnify  the  image 
so  that  the  angular  dimensions  of  the  thing  looked  at  will 
appear  greater  when  the  telescope  is  used  than  when  it  is 
not. 


ASTRONOMICAL  INSTRUMENTS.  61 

For  example,  in  the  figure  suppose  BI  to 
be  a  luminous  surface.  Every  point  of  it  is 
throwing  off  rays  of  light  in  straight  lines  in 
every  possible  direction.  Let  us  consider  the 
point  /.  The  rays  from  /  proceed  in  every 
direction  in  which  we  can  draw  a  straight  line 
through  /.  Suppose  all  such  straight  lines 
drawn.  Let  00'  be  the  objective  of  a  tele- 
scope pointed  towards  BI.  All  the  rays  from 
/  which  fall  on  00'  lie  between  the  lines  10, 
and  10'.  No  others  can  reach  the  objective, 
and  all  others  which  proceed  from  /  are 
wasted  so  far  as  seeing  /  with  this  particu- 
lar telescope  is  concerned. 

The  action  of  the  convex  lens  00'  is  to 
bend  every  ray  which  passes  through  it  to- 
wards its  axi^  BA.  10  is  bent  down  to  01' \ 
10'  is  bent  up  to  OT;  and  so  for  every 
other  ray  except  the  ray  from  /  through  the 
centre  of  00'  which  is  bent  neither  up  nor 
down,  but  which  goes  straight  on  to  I'  and 
beyond. 

Every  one  of  the  rays  of  light  sent  out  by 
/between  the  limits  JO  and  10'  finally  passes 
through  /'.  /  is  a  point  of  light,  and  so  is 
/'.  The  point  /'  is  the  focus  of  00'  with 
respect  to  /. 

Similarly  B  sends  out  light  in  every  direc- 
tion. Only  those  rays  which  chance  to  fall 
between  BO  and  BO'  are  useful  for  seeing 
B  with  this  particular  telescope.  Every  one 
of  this  bundle  of  rays  comes  to  &  focus  on  the 

"FIO.  19. 


62  ASTRONOMY. 

intersection  of  the  lines  /' and  BA.  In  the  same  way 

every  point  of  the  object  .#/has  a  corresponding  image  on 

the  line  /' somewhere  between  1'  and  the  axis  BA. 

I' is  the  focal  plane  of  the  objective  with  respect  to 

the  object  BI,  and  the  image  of  BI  lies  in  this  focal  plane. 
The  objective  has  now  done  all  it  can;  it  has  gathered 
every  possible  ray  from  the  object  BI  and  presents  every 
one  of  these  rays  concentrated  in  an  image  of  this  object 
in  the  focal  plane  at  F 

Notice  two  things:  first,  the  image  is  inverted  with  re- 
spect to  the  object;  /  is  above  B;  the  image  of  /  is  below 

the  image  of  B\  second,  the  rays  from  B /do  not 

stop  at  /' ,  but  go  on  indefinitely  to  the  left,  always 

diverging  from  the  image. 

The  Eye-piece. — The  eye-piece  is  essentially  a  microscope 
which  is  simply  to  magnify  the  angular  dimensions  of  the 
object  as  it  is  seen  in  the  telescope;  that  is,  to  magnify  the 
image.  To  see  well  with  a  microscope  it  must  be  close  to 
the  thing  magnified.  It  cannot  be  placed  near  to  BI  in 
general,  for  BI  may  be  a  mile  or  ten  millions  of  miles 
away.  So  the  place  to  put  it  is  near  to  the  image  of  BI,  a 
little  above  the  focal  plane  F in  the  figure. 

The  eye  must  be  placed  a  little  further  above  still, 
at  such  a  position  as  to  see  well  with  the  eye-piece.  That 
is,  close  to  it.  Now  fix  an  objective  in  one  end  of  a  tube 
and  an  eye-piece  in  the  other  end  and  you  have  a  refracting 
telescope.  The  more  powerful  the  microscope  used  as  an 
eye-piece  the  higher  the  magnifying  power  of  the  combina- 
tion. We  increase  the  magnifying  power  of  any  telescope 
by  changing  the  eye-piece. 

The  Objective. — As  a  matter  of  fact  the  objective  is  usu- 
ally made  of  two  glasses  like  the  figure,  where  the  arrow 


ASTRONOMICAL  INSTRUMENTS.  63 

shows  the  direction  in  which  the  rays  come  to  it  from  the 
object.  If  we  use  a  dngle  ob- 
jective we  find  that  the  image  of 
the  object  is  colored ;  that  is,  of 
different  colors  from  its  natural 
tints.  We  find  that  by  using  a 
double  objective  made  of  two  FIQ.  20. 

different  kinds  of  glass  this  can  be  corrected.  This  is  ex- 
plained in  Optics  under  the  head  of  Achromatism  or  Chro- 
matic Aberration. 

Light-gathering  Power. — It  is  not  merely  by  magnifying 
that  the  telescope  assists  the  vision,  but  also  by  increasing 
the  quantity  of  light  which  reaches  the  eye  from  the  object 
at  which  we  look.  Indeed,  should  we  view  an  object 
through  an  instrument  which  magnified  but  did  not  in- 
crease the  amount  of  light  received  by  the  eye,  it  is  evident 
that  the  brilliancy  would  be  diminished  in  proportion  as 
the  surface  of  the  image  was  enlarged,  since  a  constant 
amount  of  light  would  be  spread  over  an  increased  surface; 
and  thus,  unless  the  light  were  very  bright,  the  object  might 
become  so  darkened  as  to  be  less  plainly  seen  than  with  the 
naked  eye.  How  the  telescope  increases  the  quantity  of 
light  will  be  seen  by  considering  that  when  the  unaided 
eye  looks  at  any  object,  the  retina  can  only  receive  so  many 
rays  as  fall  upon  the  pupil  of  the  eye.  By  the  use  of  the 
telescope  it  is  evident  that  as  many  rays  can  be  brought  to 
the  retina  as  fall  on  the  entire  object-glass.  The  pupil  of 
the  human  eye,  in  its  normal  state,  has  a  diameter  of  about 
one  fifth  of  «an  inch,  and  by  the  use  of  the  telescope  it  is 
virtually  increased  in  surface  in  the  ratio  of  the  square  of 
the  diameter  of  the  objective  to  the  square  of  one  fifth  of 
an  inch;  that  is?  in  the  ratio  of  the  surface  of  the  objective 


64  ASTRONOMY. 

to  the  surface  of  the  pupil  of  the  eye.  Thus,  with  a  two- 
inch  aperture  to  our  telescope,  the  number  of  rays  collected 
is  one  hundred  times  as  great  as  the  number  collected  with 
the  naked  eye. 

With  a  5-inch  object-glass  the  ratio  is      625  to  1 

"       10    "  "             "        "       2,500  to  1 

"       15    "  "             •«        "       5.625  to  1 

"       20     "  "              "        "     10  000  to  1 

"       26    "  "        "     16,900  to  1 

When  a  minute  object,  like  a  small  star,  is  viewed,  it  is 
necessary  that  a  certain  number  of  rays  should  fall  on  the 
retina  in  order  that  the  star  may  be  visible  at  all.  It  is 
therefore  plain  that  the  use  of  the  telescope  enables  an 
observer  to  see  much  fainter  stars  than  he  could  detect  with 
the  naked  eye,  and  also  to  see  faint  objects  much  better 
than  by  unaided  vision  alone.  Thus,  with  a  -20-inch  tele- 
scope we  may  see  stars  so  minute  that  it  would  rorjuire  the 
collective  light  of  many  thousands  to  be  vi.-ible  to  the 
unaided  eye. 

Eye-piece. — In  the  skeleton  form  of  telescope  before  de- 
scribed the  eye-piece  as  well  as  the  objective  was  considered 
as  consisting  of  but  a  single  lens.  But  with  such  an  eye- 
piece vision  is  imperfect,  except  in  the  centre  of  the  field, 
from  the  fact  that  the  image  does  not  throw  rays  in  every 
direction,  but  only  in  straight  lines  away  from  the  objec- 
tive. Hence  the  rays  from  near  the  edges  of  the  focal 
image  fall  on  or  near  the  edge  of  the  eye- piece,  whence 
arises  distortion  of  the  image  formed  on  the  retina,  and  loss 
of  light.  To  remedy  this  difficulty  a  lens  is  inserted  at  or 
very  near  the  place  where  the  focal  image  is  formed,  for  the 
purpose  of  throwing  the  different  pencils  of  rays  which 
emanate  from  the  several  parts  of  the  image,  toward  the 


ASTRONOMICAL  INSTRUMENTS.  65 

axis  of  the  telescope,  so  that  they  shall  all  pass  nearly 
through  the  centre  of  the  eye-lens  proper.  These  two 
lenses  are  together  called  the  eye-piece. 

There  are  some  small  differences  of  detail  in  the  con- 
struction of  eye-pieces,  but  the  general  principle  is  the 
same  in  all 

The  figure  shows  an  eye-piece  drawn  accurately  to  scale.  01  is 
one  of  the  converging  pencils  from  the  object-glass  which  forms  one 
point  (/)  of  the  focal  image  la.  This  image  is  viewed  by  the  field- 
lens  F  of  the  eye-piece  as  if  it  were  a  real  object,  and  the  shaded  pencil 
between  ^and  E  shows  the  course  of  these  rays  after  deviation  by  F. 
If  there  were  no  eye-lens  E,  an  eye  properly  placed  beyond  F  would 
see  an  image  at  1' a1.  The  eye-lens  Z£ receives  the  pencil  of  rays,  and 
deviates  it  to  the  observer's  eye  placed  at  such  a  point  that  the  whole 
incident  pencil  will  pass  through  the  pupil  and  fall  on  the  retina,  and 
thus  be  effective.  As  we  saw  in  the  figure  of  the  refracting  telescope, 


FIG  21. 

every  point  of  the  object  produces  a  pencil  similar  to  01,  and  the 
whole  surfaces  of  the  lenses  Faud  J57are  covered  with  rays.  All  of 
these  pencils  passing  through  the  pupil  go  to  make  up  the  retinal 
image.  This  image  is  referred  by  the  mind  to  the  distance  of  distinct 
vision  (about  ten  inches),  and  the  image  AF'  represents  the  dimen- 
sion of  the  final  image  relative  to  the  ima^e  al  as  formed  by  the  ob- 

AI" 
jective,  and  — —  is  evidently  the  magnifying  power  of  this  particular 

Ob  J. 

eye-piece  used  in  combination  with  this  particular  objective. 


66  ASTRONOMY. 

Reflecting  Telescopes. — As  we  have  seen,  one  essential  part  of  a 
refracting  telescope  is  the  objective,  which  brings  all  the  incident  rays 
from  an  object  to  one  focus,  forming  there  an  image  of  that  object 
In  reflecting  telescopes  (reflectors)  the  objective  is  a  mirror  of  specu- 
lum metal  or  silvered  glass  ground  to  the  shape  of  a  paraboloid.  The 
figure  shows  the  action  of  such  a  mirror  on  a  bundle  of  parallel  rays, 
which,  after  impinging  on  it,  are  brought  by  reflection  to  one  focus 
F.  The  image  formed  at  this  focus  may  be  viewed  with  an  eye- 
piece, as  in  the  case  of  the  refracting  telescope. 

The  eye-pieces  used  with  such  a  mirror  are  of  the  kind  already 
described.  In  the  figure  the  eye-piece  would  have  to  be  placed  to 


Fio.  22. 

the  right  of  the  point  F,  and  the  observer's  head  would  thus  interfere 
with  the  incident  light.  Various  devices  have  been  proposed  to  rem- 
edy this  inconvenience,  of  which  the  most  simple  is  to  interpose  a 
small  plane  mirror,  which  is  inclined  45°  to  the  line  AC,  just  to  the 
left  of  F.  This  mirror  will  reflect  the  rays  which  are  moving  towards 
the  focus  ^down  (in  the  figure)  to  another  focus  outside  of  the  main 
beam  of  rays.  At  this  second  focus  the  eye-piece  is  placed  and  the 
observer  looks  into  it  in  a  direction  perpendicular  to  AG. 

The  Telescope  in  Measurement, — A  telescope  is  generally 
thought  of  only  as  an  instrument  to  assist  the  eye  by  its 
magnifying  and  light-gathering  power  in  the  manner  we 
have  described.  But  it  has  a  very  important  additional 
function  in  astronomical  measurements  by  enabling  the 
astronomer  to  point  at  a  celestial  object  with  a  certainty 
and  accuracy  otherwise  unattainable.  This  function  of 
the  telescope  was  not  recognized  for  more  than  half  a  cen- 


ASTRONOMICAL  INSTRUMENTS.  57 

tury  after  its  invention,  and  after  a  long  and  rather  acri- 
monious contest  between  two  schools  of  astronomers. 
Until  the  middle  of  the  seventeenth  century,  when  an 
astronomer  wished  to  determine  the  altitude  of  a  celestial 
object,  or  to  measure  the  angular  distance  between  two 
stars,  he  was  obliged  to  point  his  sextant  or  other  meas- 
uring instrument  at  the  object  by  means  of  "pinnules." 
These  served  the  same  purpose  as  the  sights  on  a  rifle.  In 
using  them,  however,  a  difficulty  arose.  It  was  impossible 
for  the  observer  to  have  distinct  vision  both  of  the  object 
and  of  the  pinnules  at  the  same  time,  because  when  the 
eye  was  focused  on  either  pinnule,  or  on  the  object,  it  was 
necessarily  out  of  focus  for  the  others.  The  only  way  to 
diminish  this  difficulty  was  to  lengthen  the  arm  on  which . 
the  pinnules  were  fastened  so  that  the  latter  should  be  as 
far  apart  as  possible.  Thus  TYCHO  BRAHE,  before  the 
year  1600,  had  measuring  instruments  very  much  larger 
than  any  in  use  at  the  present  time.  But  this  plan  only 
diminished  the  difficulty  and  could  not  entirely  obviate  it, 
because  to  be  manageable  the  instrument  must  not  be  very 
large. 

About  1670  the  English  and  French  astronomers  found 
that  by  simply  inserting  fine  threads  or  wires  exactly  in 
the  focus  of  the  object-glass,  and  then  pointing  it  at  the 
object,  the  image  of  that  object  formed  in  the  focus  could 
be  made  to  coincide  with  the  threads,  so  that  the  observer 
could  see  the  two  exactly  superimposed  upon  each  other. 
When  thus  brought  into  coincidence,  it  was  obvious  that 
the  point  of  the  object  on  which  the  wires  were  set  was  in 
a  straight  line  passing  through  the  wires,  and  through  the 
centre  of  the  object-glass.  So  exactly  could  such  a  point- 
ing be  made,  that  if  the  telescope  did  not  magnify  at  all 


68  ASTRONOMY. 

(the  eye-piece  and  object-glass  being  of  equal  focal  length), 
a  very  important  advance  would  still  be  made  in  the  ac- 
curacy of  astronomical  measurements.  This  line,  passing 
centrally  through  the  telescope,  we  call  the  line  of  colli- 
mation  of  the  telescope,  A  B  in  Fig.  19.  If  we  have  any 
way  of  determining  it,  it  is  as  if  we  had  an  indefinitely  long 
pencil  extended  from  the  earth  to  the  sky.  If  the  observer 
simply  sets  his  telescope  in  a  fixed  position,  looks  through 
it  and  notices  what  stars  pass  along  the  threads  in  the  eye- 
piece, he  knows  that  all  those  stars  lie  in  the  axis  of  col- 
limation  of  his  telescope  at  that  instant, 

By  the  diurnal  motion  a  pencil-mark,  as  it  were,  is  thus 
drawn  on  the  surface  of  the  celestial  sphere  among  the 
stars,  and  the  direction  of  this  pencil-mark  can  be  deter- 
mined with  far  greater  precision  by  the  telescope  than  with 
the  naked  eye. 

CHRONOMETERS  AND  CLOCKS, 

We  have  seen  that  it  is  important  for  various  purposes 
that  an  observer  should  be  able  to  determine  his  local  time 
(see  page  52).  This  local  time  is  determined  most  accu- 
rately by  observing  the  transits  of  stars  over  the  celestial 
meridian  of  the  place  where  the  observer  is.  In  order  to 
determine  the  moment  of  transit  with  all  required  accuracy, 
it  is  necessary  that  the  time-pieces  by  which  it  is  measured 
shall  go  with  the  greatest  possible  precision.  There  is  no 
great  difficulty  in  making  astronomical  measures  to  a  sec- 
ond of  arc,  and  a  star,  by  its  diurnal  motion,  passes  over 
this  space  in  one  fifteenth  of  a  second  of  time  (see  page 
44).  It  is  therefore  desirable  that  the  astronomical  clock 
shall  not  vary  from  a  uniform  rate  more  than  a  few 


ASTRONOMICAL  INSTRUMENTS.  69 

hundredth s  of  a  second  in  the  course  of  a  day.  It  is 
not,  however,  necessary  that  it  should  always  be  perfectly 
correct;  it  may  go  too  fast  or  too  slow  without  detracting 
from  its  character  for  accuracy,  if  the  intervals  of  time 
which  it  tells  off — hours,  minutes,  or  seconds — are  always 
of  exactly  the  same  length,  or,  in  other  words,  if  it  gains 
or  loses  exactly  the  same  amount  every  hour  and  every 
day. 

The  time-pieces  used  in  astronomical  observation  are  the 
chronometer  and  the  clock. 

The  chronometer  is  merely  a  very  perfect  watch  with 
a  balance-wheel  so  constructed  that  changes  of  tempera- 
ture have  the  least  possible  effect  upon  the  time  of  its 
oscillation.  Such  a  balance  is  called  a  condensation  bal- 
ance. 

The  ordinary  house-clock  goes  faster  in  cold  than  in 
warm  weather,  because  the  pendulum-rod  shortens  under 
the  influence  of  cold.  This  effect  is  such  that  the  clock 
will  gain  about  one  second  a  day  for  every  fall  of  3°  Cent. 
(5°. 4  Fahr.)  in  the  temperature,  supposing  the  pendulum- 
rod  to  be  of  iron.  Such  changes  of  rate  would  be  entirely 
inadmissible  in  a  clock  used  for  astronomical  purposes. 
The  astronomical  clock  is  therefore  provided  with  a  com- 
pensation pendulum,  by  which  the  disturbing  effects  of 
changes  of  temperature  are  avoided. 

The  correction  of  a  clock  is  the  quantity  which  it  is  necessary  to 
add  to  the  indications  of  the  hands  to  obtain  the  true  time.  Thus  if 
the  correction  of  a  sidereal  clock  is  -f-  lm  10s.  07  and  the  hands  point 
to  21h  13m  14". 50,  the  correct  sidereal  time  is  21h  14m  24s. 57. 

The  rate  of  a  clock  is  the  daily  change  of  its  correction;  i.e.,  what 
it  gains  or  loses  daily. 


70 


ASTRONOMY. 


THE  TRANSIT  INSTRUMENT. 

The  Transit  Instrument  is  used  to  observe  the  transits 
of  stars  over  the  celestial  meridian.     The  times  of  these 


FIG.  23. 


transits  are  noted  by  the  sidereal  clock,  which  is  an  indis- 
pensable adjunct  of  the  transit  instrument. 


ASTRONOMICAL  INSTRUMENTS.  71 

It  consists  essentially  of  a  telescope  TT  mounted  on  an  axis  VV 
at  right  angles  to  it.  The  ends  of  this  axis  terminate  in  accurately 
cylindrical  pivots  which  rest  in  metallic  bearings  VV  which  are 
shaped  like  the  letter  Y,  and  hence  called  the  Y's. 

These  are  fastened  to  two  pillars  of  stone,  brick,  or  iron.  Two 
counterpoises  TFTFare  connected  with  the  axis  as  in  the  plate,  so  as 
to  take  a  large  portion  of  the  weight  of  the  axis  and  telescope  from 
the  Y's,  and  thus  to  diminish  the  friction  upon  these  and  to  render 
the  rotation  about  V  V  more  easy  and  regular.  In  the  ordinary  use 
of  the  transit,  the  line  V  V  is  placed  accurately  level  and  also  perpen- 
dicular to  the  meridian,  or  in  the  east  and  west  line.  To  effect  this 
"adjustment"  there  are  two  sets  of  adjusting  screws,  by  which  the 
ends  of  F  Fin  the  Y's  may  be  moved  either  up  and  down,  or  north 
and  south.  The  plate  gives  the  form  of  transit  used  in  permanent 
observatories,  and  shows  the  observing  chair  C,  the  reversing  carriage 
R,  and  the  level  L.  The  arms  of  the  latter  have  Y's,  \\lrcli  can  be 
placed  over  the  pivots  FF. 

The  line  of  cottimalion  of  the  transit,  telescope  is  the  line  drawn 
through  the  centre  of  the  objective  perpendicular  to  the  rotation 
axis  VV, 

The  reticle  is  a  network  of  fine  spider-lines  placed  in  the  focus  of 
the  objective. 

In  Fig.  24  the  circle  represents  the  field  of  view  of  a  transit  as  seen 
through  the  eye-piece.  The  seven  vertical 
lines,  I,  II,  III,  IV,  V,  VI,  VII,  are  seven 
fine  spider-lines  tightly  stretched  across  a 
hole  in  a  metal  plate,  and  so  adjusted  as 
to  be  perpendicular  to  the  direction  of  a 
star's  apparent  diurnal  motion.  The  hori- 
zontal wires,  guide-wires,  a  and  b,  mark  the 
centre  of  the  field.  The  field  is  illuminated 
at  night  by  a  lamp  at  the  end  of  the  axis 
which  shines  through  the  hollow  interior  of 
the  latter,  and  causes  the  field  to  appear 
bright.  The  wires  are  dark  against  a  bright 

ground.     The  line  of  sight  is  a  line  joining  the  centre  of  the  objective 
and  the  central  one,  IV,  of  the  seven  vertical  wires. 

The  whole  transit  is  in  adjustment  when,  first,  the  axis  FFis 
horizontal ;  second,  when  it  lies  east  and  west ;  and  third,  when  the 
line  of  sight  and  the  line  of  collimation  coincide.  When  these  condi- 
tions are  fulfilled  the  line  of  sight  intersects  the  celestial  sphere  in  the 
meridian  of  the  place,  and  when  TT  is  rotated  about  F  Fthe  line  of 
sight  marks  out  the  celestial  meridian  of  the  place  on  the  sphere. 


72  ASTRONOMY. 

The  clock  stands  near  the  transit  instrument.  The  times 
when  a  star  passes  the  wires  I-VII  are  noted.  The  average 
of  these  is  the  time  when  the  star  was  on  the  middle  thread, 
or,  what  is  the  same  thing,  on  the  celestial  meridian.  At 
that  instant  its  hour-angle  is  zero.  (See  page  39.) 

The  sidereal  time  at  that  instant  is  the  hour-angle  of  the 
vernal  equinox  (see  page  44).  This  is  measured  from  the 
meridian  towards  the  west.  The  right  ascension  of  the 
star  which  is  observed  is  the  same  quantity,  measured  from 
the  vernal  equinox  towards  the  east.  As  the  star  is  on 
the  meridian,  the  two  are  equal.  Suppose  we  know  the 
right  ascension  of  the  star  and  that  it  is  a.  Suppose  the 
clock  time  of  transit  is  T.  It  should  have  been  a  if  the 
clock  were  correct.  The  correction  of  the  clock  at  this 
instant  is  thus  a  —  T. 

This  is  the  use  we  make  of  stars  of  known  right  ascen- 
sions. By  observing  any  one  of  them  we  can  get  a  value  of 
the  clock  correction. 

Suppose  the  clock  to  be  correct,  and  suppose  we  note  that 
a  star  whose  right  ascension  is  unknown  is  on  the  wire  IV 
at  the  time  a'  by  the  clock,  a'  is  then  the  right  ascension 
of  that  star.  In  this  way  the  positions  of  stars,  or  of  the 
sun  and  planets  (in  right  ascension  only),  are  determined, 

THE  MERIDIAN  CIRCLE. 

The  meridian  circle  is  a  combination  of  the  transit  in- 
strument with  a  graduated  circle  fastened  to  its  axis  and 
moving  with  it.  A  meridian  circle  is  shown  hi  Fig.  25. 
It  has  two  circles  finely  divided  on  their  sides.  The  grad- 
aatiou  of  each  circle  is  viewed  by  four  microscopes.  The 
microscopes  are  90°  apart.  The  cut  shows  also  the  hang- 
ing level  by  which  the  error  of  level  of  the  axis  is  found. 


ASTRONOMICAL  INSTRUMENTS. 


73 


The  instrument  can  be  used  as  a  transit  to  determine 
right  ascensions,  as  before  described.  It  can  be  also  used 
to  measure  declinations  in  the  following  way  :  If  the 
telescope  is  pointed  to  the  nadir,  a  certain  division  of 


FIG.  25. 

the  circles,  as  N,  is  under  the  first  microscope.*  "We  can 
make  the  nadir  a  visible  point  by  placing  a  basin  of  quick- 
silver below  the  telescope  and  looking  in  it  through  the  tel- 
escope. We  shall  see  the  wires  of  the  reticle  and  also  their 

*  Or  opposite  to  a  stationary  pointer  fixed  to  the  pier. 


74  ASTliONOMY. 

reflected  images  in  the  quicksilver.  When  these  coincide, 
the  telescope  points  to  the  nadir.  If  it  is  then  pointed  to 
the  pole,  the  reading  will  change  by  the  angular  distance 
between  the  nadir  and  the  pole,  or  by  90°  -\-  g>,  (p  being  the 
latitude  of  the  place  (supposed  to  be  known).  The  polar 
reading  P  of  the  circle  is  thus  known  when  the  nadir 
reading  Nia  found.  If  the  telescope  is  then  pointed  to 
various  stars  of  unknown  polar  distances,  ;/,  p",  p'",  etc., 
as  they  successively  cross  the  meridian,  and  if  the  circle 
readings  for  these  stars  are  P',  P",  P'",  etc.,  it  follows 
that  p'=P'—P;  p"  =  P"—  P;  p'"  =  P'"  —  P;  etc. 

Thus  the  meridian  circle  serves  to  determine  by  observa- 
tion loth  co-ordinates  of  the  apparent  position  of  a  body. 

THE  EQUATORIAL. 

An  equatorial  telescope  is  one  mounted  in  such  a  way  that 
a  star  may  be  followed  through  its  diurnal  orbit  by  turning 
the  telescope  about  one  axis  only.  The  equatorial  mount- 
ing consists  essentially  of  a  pair  of  axes  at  right  angles 
to  each  other.  One  of  these  S  N  (the  polar  axis)  is  direct- 
ed toward  the  elevated  pole  of  the  heavens,  and  it  there- 
fore makes  an  angle  with  the  horizon  equal  to  the  latitude 
of  the  place  (p.  31).  This  axis  can  be  turned  about  its  own 
axial  line.  On  one  extremity  it  carries  another  axis  LD 
(the  declination  axis),  which  is  fixed  at  right  angles  to  it, 
but  which  can  again  be  rotated  about  its  axial  line. 

To  this  last  axis  a  telescope  is  attached,  which  may  either 
be  a  reflector  or  a  refractor.  It  is  plain  that  such  a  tele- 
scope may  be  directed  to  any  point  of  the  heavens;  for  we 
can  rotate  the  declination  axis  until  the  telescope  points  to 
any  given  polar  distance  or  declination.  Then,  keeping 
the  telescope  fixed  in  respect  to  the  declination  axis,  we  can 


ASTRONOMICAL  INSTRUMENTS.  75 


FIG.  26. 


76  ASTRONOMY. 

rotate  the  whole  instrument  as  one  mass  about  the  polar 
axis  until  the  telescope  points  to  any  portion  of  the  parallel 
of  declination  defined  by  the  given  right  ascension  or  hour- 
angle.  Fig.  20  is  an  equatorial  of  9J-inch  aperture,  with 
driving-clock  inside  the  pedestal. 

If  we  point  such  a  telescope  to  a  star  when  it  is  rising  (doing  this 
by  rotating  the  telescope  first  about  its  declination  axis  and  then 
about  the  polar  axis),  and  fix  the  telescope  in  this  position,  we  can, 
by  simply  rotating  the  whole  apparatus  on  the  polar  axis,  cause  the 
telescope  to  trace  out  on  the  celestial  sphere  the  apparent  diurnal 
path  which  this  star  will  appear  to  follow  from  rising  to  setting.  In 
such  telescopes  a  driving-clock  is  so  arranged  that  it  can  turn  the 
telescope  round  the  polar  axis  at  the  same  rate  at  which  the  earth  it- 
self turns  about  its  own  axis  of  rotation,  but  in  a  contrary  direction. 
Hence  such  a  telescope  once  pointed  at  a  star  will  continue  to  point 
at  it  as  long  as  the  driving-clock  is  in  operation,  thus  enabling  the 
astronomer  to  make  such  an  examination  or  observation  of  it  as  is 
required. 

THE  SEXTANT. 

The  sextant  is  a  portable  instrument  by  which  the  altitudes  of 
celestial  bodies  or  the  angular  distances  between  them  may  be 
measured.  It  is  used  chiefly  by  navigators  for  determining  the  lati- 
tude and  the  local  time  of  the  position  of  the  ship.  Knowing  the 
local  time,  and  comparing  it  with  a  chronometer  regulated  on  Green- 
wich time,  the  longitude  becomes  known  and  the  ship's  place  is 
fixed.  (See  page  52.) 

It  consists  of  an  arc  of  a  divided  circle  usually  60°  in  extent, 
whence  the  name.  This  arc  is  in  fact  divided  into  120  equal  parts, 
each  marked  as  a  degree,  and  these  are  again  divided  into  smaller 
spaces,  so  that  by  means  of  the  vernier  at  the  end  of  the  index  arm 
MS  an  arc  of  10"  (usually)  may  be  read. 

The  index-arm  MS  carries  the  index-glass  M,  which  is  a  silvered 
plane  mirror  set  perpendicular  to  the  plane  of  the  divided  arc.  The 
horizon-glass  m  is  also  a  plane  mirror  fixed  perpendicular  to  the  plane 
of  the  divided  circle. 

This  last  glass  is  fixed  ia  position,  while  the  first  revolves  with  the 
index-arm.  The  horizon-glass  is  divided  into  two  parts,  of  which 
the  lower  one  is  silvered,  the  upper  half  being  transparent.  E  is  a 
telescope  of  low  power  pointed  toward  the  horizon- glass.  By  it  any 


ASTRONOMICAL  INSTRUMENTS. 


77 


object  to  which  it  is  directly  pointed  can  be  seen  through  the  unsilvered 
half  of  the  horizon-glass.  Any  other  object  in  the  same  plane  can  be 
brought  into  the  same  field  by  rotating  the  index-arm  (and  the  index- 
glass  with  it),  so  that  a  beam  of  light  from  this  second  object  shall 
strike  the  index-glass  at  the  proper  angle,  there  to  be  reflected  to  the 
horizon -glass,  and  again  reflected  down  the  telescope  E.  Thus  the 
images  of  any  two  objects  in  the  plane  of  the  sextant  may  be  brought 
together  in  the  telescope  by  viewing  one  directly  and  the  other  by 
reflection. 


Fro.  27. 

This  instrument  is  used  daily  at  sea  to  determine  the 
ship's  position  by  measuring  the  altitude  of  the  sun.  This 
is  done  by  pointing  the  telescope,  E  J9,  to  the  sea-horizon, 
H  in  the  figure,  which  appears  like  a  line  in  the  field  of  the 
telescope,  and  by  moving  the  index-arm  till  the  image  of 


78  ASTRONOMY. 

the  sun,  S,  coincides  with  the  horizon.  The  arc  read  from 
the  sextant  at  this  time  is  the  sun's  altitude.  From  the 
altitude  of  the  sun  on  the  meridian  the  ship's  latitude  is 
known  (see  page  54).  From  its  altitude  at  another  hour 


Fio 


the  local  time  can  be  computed.  The  difference  between 
the  local  time  and  the  Greenwich  time,  as  shown  by  the 
ship's  chronometer,  gives  the  ship's  longitude.  By  means 
of  this  simple  instrument  the  place  of  a  vessel  can  be  found 
witnin  a  mile  or  so. 

The  above  are  the  instruments  of  astronomy  which  best 
illustrate  the  principles  of  astronomical  observations. 

Practical  Astronomy  is  the  science  which  teaches  the 
theory  of  these  instruments  and  of  their  application  to  ob- 
servation, and  it  includes  the  art  of  so  combining  the 
observations  and  so  using  the  appliances  as  to  get  the  best 
results. 


ASTRONOMICAL  EPHEMERIS.  79 


THE  ASTRONOMICAL  EPHEMERIS,  OB  NAUTICAL  ALMANAC, 

The  Astronomical  Ephemeris,  or,  as  it  is  more  commonly  called, 
the  Nautical  Almanac,  is  a  work  in  which  celestial  phenomena  and 
the  positions  of  the  heavenly  bodies  are  computed  in  advance. 

The  usefulness  of  such  a  work,  especially  to  the  navigator,  de- 
pends upon  its  regular  appearance  on  a  uniform  plan  and  upon  the 
fulness  and  accuracy  of  its  data;  it  was  therefore  necessary  that  its 
i'ssue  should  be  taken  up  as  a  government  work.  An  astronomical 
ephemeris  or  nautical  almanac  is  now  published  annually  by  each  of 
the  governments  of  Germany,  Spain,  Portugal,  France,  Great  Britain, 
and  the  United  States.  They  are  printed  three  years  or  more  be- 
forehand, in  order  that  navigators  going  on  long  voyages  may  supply 
themselves  in  advance. 

The  Ephemeris  furnishes  the  fundamental  data  from  which  all  our 
household  almanacs  are  calculated. 

The  principal  quantities  given  in  the  American  Ephemeris  for 
each  year  are  as  follows: 

The  positions  (R.  A.  and  8)  of  the  sun  and  the  principal  large 
planets  for  Greenwich  noon  of  every  day  in  each  year. 

The  right  ascension  and  declination  of  the  moon's  centre  for  every 
Greenwich  hour  in  the  year. 

The  distance  of  the  moon  from  certain  bright  stars  and  planets  for 
every  third  Greenwich  hour  of  the  year. 

The  right  ascensions  and  declinations  of  upward  of  two  hundred 
of  the  brighter  fixed  stars,  corrected  for  precession,  nutation,  and 
aberration,  for  every  ten  days. 

The  positions  of  the  principal  planets  at  every  visible  transit  over 
the  meridian  of  Washington. 

Complete  elements  of  all  the  eclipses  of  the  sun  and  moon,  with 
maps  showing  the  passage  of  the  moon's  shadow  or  penumbra  over 
those  regions  of  the  earth  where  the  eclipses  will  be  visible,  and 
tables  whereby  the  phases  of  the  eclipses  can  be  accurately  computed 
for  any  place. 

Tables  for  predicting  the  occultations  of  stars  by  the  moon. 

Eclipses  of  Jupiter's  satellites  and  miscellaneous  phenomena. 

Catalogues  of  Stars. — Of  the  same  general  nature  with  the  Ephe- 
meris are  catalogues  of  the  fixed  stars.  The  object  of  such  a  cata- 
logue is  to  give  the  right  ascension  and  declination  of  a  number  of 
stars  for  some  epoch,  the  beginning  of  the  year  1875  for  instance, 
with  the  data  by  which  the  position  of  each  star  can  be  found  at  any 
other  epoch. 


80 


ASTRONOMY. 


To  give  the  student  a  still  further  idea  of  the  Ephemeris,  we  present 
a  small  portion  of  one  of  its  pages  for  the  year  1882 : 

FEBRUARY,  1882— AT  GREENWICH  MEAN  NOON. 


1 

I'   i  1  licit  JMI1 

.  ! 

Ijg  . 

THE  SUN'S 

or  time 

jj 

Sidereal 

the 
week. 

I1 

to  be 
subtracted 
from 
mean 
time. 

i 

time 
or  right 
ascension 
of 
mean  sun. 

Apparent 
Bright 
ascension. 

Diff. 
forl 
hour. 

Apparent 
declination. 

Diff. 
forl 
hour. 

B.    M.        8. 

8. 

e        /           • 

. 

M.         8. 

8. 

H.     M.      8. 

Wed. 

1 

21     0    13.04  10.175 

S17     2    22.4 

+42.82    18    51.34 

0.31820   46  21.70 

Thur. 

2 

21     4    16.8410.141 

16    45      5.4 

43.57    13    58.58 

0.28420    50  18.26 

Frid. 

8 

21     8    19.82 

10.107 

16    27    30.9 

44.30 

14     5.01 

0.250 

20   54  14.81 

Sat 

4 

21   12   21  98 

10.073 

16      9    39.2 

+44.99 

14    10.61 

0.216 

20   58  11.87 

Sun. 

5 

21   16    23  33  10.040 

15    51    808 

4:,  »;-.» 

14    15.41 

0.18J21      2     7.92 

MOD. 

6 

21  20   23.88 

10.007 

15    33      6.1 

46.36 

14    19.40 

0.150 

21     6     4.48 

Tues. 

7 

21  24   23  63 

9.974 

15    14    25.4 

+47.03 

14    22  60 

0.117 

21    10     1.03 

Wed. 

8 

21   28    22  60    9.941 

14    55    29.1 

47  66 

14    25  01 

008421    13  57.59 

Thur. 

9 

21  82   20  79 

'.I.'JW 

14    36    17.7 

48.28 

14    26.65 

0.052 

21    17  54.14 

Frid. 

10 

21   36    18.21 

9.877 

14    16    51.6 

48.88 

14    27.51 

0.020 

21    21   50  70 

Sat. 

11 

21  40    14.88 

it  sic, 

13    57    11.2 

49  47 

14    27.  63 

0.011  21    25  47.25 

Sun. 

12 

21  44    10.80 

9.8n 

13    37    16.9 

50.03 

14    26.99 

0.042 

21    29  43.81 

Mon. 

13 

21  48     5.98 

9.784 

13    17      91 

+50.59 

14    25.63 

0  073 

21    33  40  35 

Tues. 

14 

21  52     0.43 

I.7H 

12    56    48  8 

51.12    14    2:1  M 

0.10421    37  36.91 

Wed. 

15 

21  55   54.16 

9.723 

12    36    14.9 

51.65    14    20.70 

0.134 

21    41   33  46 

Thur. 

16 

21  59   47.17 

MM 

12    15    29.3 

+52.14 

14    17.15 

0  164 

21    45  30.02 

Frid. 

17 

22     3   89.47 

-.)  mi 

11    54    82  1 

V>  A*> 

14    12  90 

0  19321    49  26.57 

Sat. 

18 

22     7   31.07 

9.635 

11    33    M  i; 

53^07 

14      7.94 

022221    58  23.13 

1 

The  third  column  shows  the  R.  A.  of  the  sun's  centre  at  Green- 
wich mean  noon  of  each  day.  The  fourth  column  shows  the  hourly 
change  of  this  quantity  (9.815  on  Feb.  12).  At  Greenwich  0  hours 
the  sun's  R.  A.  was  21 h  44m  lO'.SO.  Washington  is  5h  8m  (5M3) 
west  of  Greenwich.  At  Washington  mean  noon,  on  the  12th.  the 
Greenwich  mean  time  was  5h.  13.  9.815  X  5.13  is  50'.35.  This  is  to 
be  added,  since  the  R.  A.  is  increasing.  The  sun's  R.  A.  at  Wash- 
ington mean  noon  is  therefore  21h  45m  1".  15.  A  similar  process  will 
give  the  sun's  declination  for  Washington  mean  noon.  In  the  same 
manner,  theR.  A.  and  Dec.  of  the  sun  for  any  place  whose  longitude 
is  known  can  be  found. 

The  column  "Equation  of  Time"  gives  the  quantity  to  be  sub- 
tracted from  the  Greenwich  mean  solar  time  to  obtain  the  Green- 
wich apparent  solar  time  (see  page  188).  Thus,  for  Feb.  1,  the 
Greenwich  mean  time  of  Greenwich  mean  noon  is  Oh  0™  0*.  The 
true  sun  crossed  the  Greenwich  meridian  (apparent  noon)  at  23h  46m 
08*. 66  on  the  preceding  day;  i.e.,  Jan.  31. 

When  it  was  Oh  Om  6s  of  Greenwich  mean  time  on  Feb.  13.  it  was 
also  21h  33m  40».35  of  Greenwich  local  sidereal  time  (see  the  last 
column  of  the  table). 


CHAPTER  IV. 
MOTION  OF  THE  EARTH. 

ANCIENT  IDEAS  OF  THE  PLANETS. 

IT  was  observed  by  the  ancients  that  while  the  great 
mass  of  the  stars  maintained  their  positions  relatively  to 
each  other  month  after  month  and  year  after  year,  there 
were  visible  to  them  seven  heavenly  bodies  which  cJianged 
their  positions  relatively  to  the  stars  and  to  each  other. 
These  they  called  planets  or  wandering  stars.  It  was  found 
that  the  seven  planets  performed  a  very  slow  revolution 
around  the  celestial  sphere  from  west  to  east,  in  periods 
ranging  from  one  month  in  the  case  of  the  moon  to  thirty 
years  in  that  of  Saturn. 

The  idea  of  the  fixed  stars  being  set  in  a  solid  sphere  was 
in  perfect  accord  with  their  diurnal  revolution  as  observed 
by  the  naked  eye.  But  it  was  not  so  with  the  planets. 
The  latter,  after  continued  observation,  were  found  to 
move  sometimes  backward  and  sometimes  forward;  and  it 
was  quite  evident  that  at  certain  periods  they  were  nearer 
the  earth  than  at  other  periods.  These  motions  were  en- 
tirely inconsistent  with  the  theory  that  they  were  fixed  in 
solid  spheres. 

These  planets  (which  are  visible  to  the  naked  eye), 
together  with  the  earth,  and  a  number  of  other  bodies 
which  the  telescope  has  made  known  to  us,  form  a  family 
or  system  by  themselves,  the  dimensions  of  which,  although 


82  ASTRONOMY. 

inconceivably  greater  than  any  which  we  have  to  deal  with 
at  the  surface  of  the  earth,  are  quite  insignificant  when 
compared  with  the  distance  which  separates  us  from  the 
fixed  stars.  The  sun  being  the  great  central  body  of  this 
system,  it  is  called  the  Solar  System.  There  are  eight 
large  planets,  of  which  the  earth  is  the  third  in  the  order  of 
distance  from  the  sun,  and  these  bodies  all  perform  a  regular 
revolution  around  the  sun.  Mercury,  the  nearest,  performs 
its  revolution  in  three  months ;  Neptune,  the  farthest,  in 
164  years. 

ANNUAL  REVOLUTION  OF  THE  EARTH. 

To  an  observer  on  the  earth  the  sun  seems  to  perform 
an  annual  revolution  among  the  stars,  a  fact  which  has 
been  known  from  early  ages.  This  motion  is  due  to  the 
annual  revolution  of  the  earth  round  the  sun. 

In  Fig.  29  let  S  represent  the  sun,  ABCD  the  orbit 
of  the  earth  around  it,  and  E FGH  the  sphere  of  the 
fixed  stars.  This  sphere,  being  supposed  infinitely  distant, 
must  be  considered  as  infinitely  larger  than  the  circle 
ABCD.  Suppose  now  that  1,  2,  3,  4,  5,  6  are  a  number 
of  consecutive  positions  of  the  earth  in  its  orbit.  The  line 
IS  drawn  from  the  sun  to  the  earth  in  any  given  position  is 
called  the  radius-vector  of  the  earth.  Suppose  this  line 
extended  infinitely  so  as  to  meet  the  celestial  sphere  in  the 
point  1'.  It  is  evident  that  to  an  observer  on  the  earth  at 
1  the  sun  will  appear  projected  on  the  sphere  in  the  direc- 
tion of  1';  when  the  earth  reaches  2  it  will  appear  in  the 
direction  of  2',  and  so  on.  In  other  words,  as  the  earth 
revolves  around  the  sun,  the  latter  will  seem  to  perform  a 
revolution  among  the  fixed  stars,  which  are  immensely 
more  distant  than  itself.  The  points  1',  2',  etc.,  can  be 


MOTIONS  OF  THE  EARTH.  83 

fixed  by  their  relations  to  the  various  fixed  stars,  whose 
places  are  known. 

It  is  also  evident  that  the  point  in  which  the  earth  would 
be  projected  if  viewed  from  the  sun  is  always  exactly 
opposite  that  in  which  the  sun  appears  as  projected  from 
the  earth.  Moreover,  if  the  earth  moves  more  rapidly  in 


Fio.  29.— REVOLUTION  OF  THE  EARTH. 

some  points  of  its  orbit  than  in  others,  it  is  evident  that 
the  sun  will  also  appear  to  move  more  rapidly  among  the 
stars,  and  that  the  two  motions  must  always  accurately 
correspond  to  each  other. 

The  radius-vector  of  the  earth  in  its  annual  course  de- 
Bribes  a  plane,  which  in  the  figure  may  be  represented  by 


84  ASTRONOMY. 

that  of  the  paper.  This  plane  continued  to  infinity  in 
every  direction  will  cut  the  celestial  sphere  in  a  great  cir- 
cle ;  and  it  is  clear  that  the  sun  will  always  appear  to 
move  in  this  circle.  The  plane  and  the  circle  are  indiffer- 
ently termed  the  ecliptic.  The  plane  of  the  ecliptic  is  gen- 
erally taken  as  the  fundamental  one,  to  which  the  positions 
of  all  the  bodies  in  the  solar  system  are  referred.  It 
divides  the  celestial  sphere  into  two  equal  parts.  In  think- 
ing of  the  celestial  motions,  it  is  convenient  to  conceive  of 
this  plane  as  horizontal.  Then  if  we  draw  a  vertical  line 
through  the  sun  at  right  angles  to  this  plane  (perpendicular 
to  the  plane  of  the  paper  on  which  the  figure  is  represent- 
ed), the  point  at  which  this  line  intersects  the  celestial 
sphere  will  be  the  pole  of  the  ecliptic. 

Let  us  now  study  the  apparent  annual  revolution  of  the 
sun  produced  by  the  real  revolution  of  the  earth  in  its  orbit. 

When  the  earth  is  at  1  in  the  figure  the  sun  will  appear 
to  be  at  1',  near  some  star,  as  drawn.  Now  by  the  diurnal 
motion*  of  the  earth  the  sun  is  made  to  rise,  to  culminate, 
and  to  set  successively  for  each  meridian  on  the  globe.  This 
star  being  near  the  sun  rises,  culminates,  and  sets  with  it; 
it  is  on  the  meridian  of  any  place  at  the  local  noon  of  that 
place  (and  is  therefore  not  visible  except  in  a  telescope).  The 
star  on  the  right-hand  side  of  the  figure  near  the  line  CSl 
prolonged  is  nearly  opposite  to  the  sun.  When  the  sun  is 
rising  at  any  place,  that  star  will  be  setting;  when  the  sun 
is  on  the  meridian  of  the  place,  this  star  is  on  the  lower 
meridian;  when  the  sun  is  setting,  this  star  is  rising.  It 
is  about  180°  from  the  sun.  Now  suppose  the  earth  to 
move  to  2.  The  sun  will  be  seen  at  2',  near  the  star  there 
marked.  2'  is  east  of  1';  the  sun  appears  to  move  among 
the  stars  (in  consequence  of  the  earth's  annual  motion) 


MOTIONS  OF  THE  EARTH.  85 

from  west  to  east.  The  star  near  2'  will  rise,  culminate, 
and  set  with  the  sun  at  every  place  on  the  earth.  The  star 
near  1'  being  west  of  2'  will  rise  "before  the  sun,  culminate 
before  him,  and  set  before  he  does. 

If,  for  example,  the  star  1'  is  near  the  equator  when  the 
sun  is  15°  east  of  1',  the  star  will  rise  about  1  hour  earlier 
than  the  sun.  When  the  sun  is  30°  east  of  1'  (at  3',  for 
example),  the  star  will  rise  2  hours  before  the  sun.  When 
the  sun  is  90°  east  of  1',  the  star  will  rise  6  hours  before  the 
,£un,  and  so  on.  That  is,  when  the  sun  is  rising  at  any 
place,  this  star  will  be  on  the  meridian  of  the  place.  When 
the  sun  appears  in  the  line  I'CS  1  prolonged  to  the  right 
in  the  figure,  the  star  1'  will  be  on  the  meridian  at  mid- 
night, and  is  then  said  to  be  in  opposition  to  the  sun.  It 
is  180°  from  it.  When  the  sun  appears  to  be  near  H,  the 
star  1'  will  be  about  45°  or  3  hours  east  of  the  sun.  The 
sun  will  rise  first  to  any  place  on  the  earth,  and  the  star 
will  rise  3  hours  later,  say  at  9  A.M.  Finally  the  sun  will 
come  back  to  the  same  star  again  and  they  will  rise,  culmi- 
nate, and  set  together. 

We  know  that  this  cycle  is  about  365  days  in  length. 
In  this  time  the  sun  moves  360°,  or  about  1°  daily.*  This 
cycle  is  perpetually  repeated.  Its  length  is  a  sidereal  year; 
that  is,  the  interval  of  time  required  for  the  sun  to  move  in 
the  sky  from  one  star  back  to  the  same  star  again,  or  for  the 
earth  to  make  one  revolution  in  its  orbit  among  the  stars. 

The  ancients  were  familiar  with  this  phenomenon.  They 
knew  most  of  the  brighter  stars  by  name.  The  heliacal 
rising  of  a  bright  star  (its  rising  with  Helios,  the  sun) 
marked  the  beginning  of  a  cycle.  At  the  end  of  it,  seasons 
and  crops  and  the  periodical  floods  of  the  Nile  had  repeat- 

*  1°  is  twice  the  sun's  apparent  diameter. 


86  A8TBQNOMT. 

ed  themselves.  It  was  in  this  way  that  the  first  accurate 
notions  of  the  year  arose. 

The  apparent  position  of  a  body  as  seen  from  the  earth 
is  called  its  geocentric  place.  The  apparent  position  of  a 
body  as  seen  from  the  sun  is  called  its  heliocentric  place. 

In  the  last  figure,  suppose  the  sun  to  be  at  #,  and  the 
earth  at  4.  4'  is  the  geocentric  place  of  the  sun,  and  G  is 
the  heliocentric  place  of  the  earth. 

THE  SUN'S  APPARENT  PATH. 

It  is  evident  that  if  the  appurmt  path  of  the  sun  lay  in 
the  equator,  it  would,  during  the  entire-  year,  rise  exactly 
in  the  east  and  set  in  the  west,  and  would  always  cross  the 
meridian  at  the  same  altitude.  The  days  would  always  be 
twelve  hours  long,  for  the  same  muson  that  a  star  in  the 
equator  is  always  twelve  hours  above  the  horizon  and  twelve 
hours  below  it.  But  we  know  that  this  is  not  the  case,  the 
sun  being  sometimes  north  of  the  equator  and  sometimes 
south  of  it,  and  therefore  it  has  a  motion  in  declination. 
To  understand  this  motion,  suppose  that  on  March  10th, 
1879,  the  sun  had  been  observed  with  a  meridian  circle  and  a 
sidereal  clock  at  the  moment  of  transit  over  the  meridian  of 
Washington.  Its  position  would  have  been  found  to  be  this: 

Right  Ascension,  23h  55m  23s;  Declination,  0°  30'  south. 
Had  the  observation  been  repeated  on  the  20th  and  fol- 
lowing days,  the  results  would  have  been: 

March  20,  R.  Ascen.  23h  59m    2s ;  Dec.  0°    6'  South. 

21,  "          Oh    2m  408 ;      "     0°  17'  North. 

22,  "          Oh    6m  19s ;      "    o°  41'  North. 

If  we  lay  these  positions  down  on  a  chart,  we  shall  find 
them  to  be  as  in  Fig.  30,  the  centre  of  the  sun  being  south 


MOTIONS  OF  THE  EARTH.  87 

of  the  equator  in  the  first  two  positions,  and  north  of  it  in 
the  last  two.  Joining  the  successive  positions  by  a  line,  we 
shall  have  a  representation  of  a  small  portion  of  the  appa- 
rent path  of  the  sun  on  the  celestial  sphere,  or  of  the  ecliptic. 
It  is  clear  from  the  observations  and  the  figure  that  the 
sun  crossed  the  equator  between  six  and  seven  o'clock  on 
the  afternoon  of  March  20th,  and  therefore  that  the  equa- 
tor and  ecliptic  intersect  at  the  point  where  the  sun  was  at 
that  hour.  This  point  is  called  the  vernal  equinox,  the 
first  word  indicating  the  season,  while  the  second  expresses 


FIG.  30.— THE  SUN  CROSSING  THE  EQUATOR. 

the  equality  of  the  nights  and  days  which  occurs  when  the 
sun  is  on  the  equator.  It  will  be  remembered  that  this 
equinox  is  the  point  from  which  right  ascensions  are  count- 
ed in  the  heavens,  in  the  same  way  that  we  count  longi- 
tudes on  the  earth  from  Greenwich  or  Washington.  A 
sidereal  clock  at  any  place  is  therefore  so  set  that  the  hands 
shall  read  0  hours  0  minutes  0  seconds  at  the  moment 
when  the  vernal  equinox  crosses  the  meridian  of  the  place. 
Continuing  our  observations  of  the  sun's  apparent  course 
for  six  months  from  March  20th  till  September  23d,  we 


ASTRONOMY. 


should  find  it  to  be  as  in  Fig.  31.     It  will  be  seen  that  Fig. 

30  corresponds  to  the  right- 
hand  end  of  31,  but  is  on  a 
much  larger  scale.  The  sun, 
moving  along  the  great  circle 
of  the  ecliptic,  will  reach  its 
greatest  northern  declination 
about  June  21st.  This  point 
is  indicated  on  the  figure  as 
90°  from  the  vernal  equinox, 
and  is  called  the  >//>/////>•/•  W- 
stice.  The  sun's  right  ascen- 
sion is  then  six  hours,  and  its 
declination  23£0  north.  The 
student  should  complete  the 
figure  by  drawing  the  half  not 
irivt-n  IKMV. 

The  course  of  the  sun  now 
inclines  toward  the  south,  and 
it  again  crosses  the  equator 
about  September  22d  at  a  point 
diametrically  opposite  the  ver- 
nal equinox.  All  great  circles 
intersect  each  other  in  two  op- 
posite points,  and  the  ecliptic 
and  equator  intersect  at  the  two 
opposite  equinoxes.  The  equi- 
nox which  the  sun  crosses  on 
September  22d  is  called  the 
autumnal  equinox. 

During  the  six  months  from 
September  to  March  the  sun's 


MOTIONS  OF  THE  EAETB.  89 

course  is  a  counterpart  of  that  from  March  to  Septem- 
ber, except  that  it  lies  south  of  the  equator.  It  attains 
its  greatest  south  declination  about  December  22d,  in 
right  ascension  18  hours  and  south  declination  23°  30'. 
This  point  is  called  the  winter  solstice.  It  then  begins  to 
incline  its  course  toward  the  north,  reaching  the  vernal 
equinox  again  on  March  20th,  1880. 

The  two  equinoxes  and  the  two  solstices  may  be  re- 
garded as  the  four  cardinal  points  of  the  sun's  apparent 
annual  circuit  around  the  heavens.  Its  passage  through 
these  points  is  determined  by  measuring  its  altitude  or  de- 
clination from  day  to  day  with  a  meridian  circle.  Since  in 
our  latitude  greater  altitudes  correspond  to  greater  declina- 
tions, it  follows  that  the  summer  solstice  occurs  on  the  day 
when  the  altitude  of  the  sun  is  greatest,  and  the  winter 
solstice  on  that  when  it  is  least.  The  mean  of  these  alti- 
tudes is  that  of  the  equator,  and  may  therefore  be  found 
by  subtracting  the  latitude  of  the  place  from  90°.  The 
time  when  the  sun  reaches  this  altitude  going  north,  marks 
the  vernal  equinox,  and  that  when  it  reaches  it  going  south 
marks  the  autumnal  equinox. 

These  passages  of  the  sun  through  the  cardinal  points  have  been 
the  subjects  of  astronomical  observation  from  the  earliest  ages  on 
account  of  their  relations  to  the  change  of  the  seasons.  An  ingeni. 
ous  method  of  finding  the  time  when  the  sun  reached  the  equinoxe*. 
was  used  by  the  astronomers  of  Alexandria  about  the  beginning  01 
our  era.  In  the  great  Alexandrian  Museum,  a  large  ring  or  whee 
was  set  up  parallel  to  the  plane  of  the  equator;  in  other  words,  it 
was  so  fixed  that  a  star  at  the  pole  would  shine  perpendicularly  01 
the  wheel.  Evidently  its  plane  if  extended  must  have  passed  througl 
the  east  and  west  points  of  the  horizon,  while  its  inclination  to  the 
vertical  was  equal  to  the  latitude  of  the  place,  which  was  not  far 
from  30°.  When  the  sun  reached  the  equator  going  north  or  south, 
and  shone  upon  this  wheel,  its  lower  edge  would  be  exactly  covered 
by  the  shadow  of  the  upper  edge;  whereas  in  any  other  position  the 


90  ASTRONOMY. 

sun  would  shine  upon  the  lower  inner  edge.  Thus  the  time  at  which 
the  sun  reached  the  equinox  could  be  determined,  at  least  to  a  frac- 
tion of  a  day.  By  the  more  exact  methods  of  modern  limes  it  can 
be  determined  within  less  than  a  minute. 

It  will  be  seen  that  this  method  of  determining  the  annual  appar- 
ent course  of  the  sun  by  its  declination  or  altitude  is  entirely  inde- 
pendent of  its  relation  to  the  fixed  stars;  and  it  could  be  equally  well 
applied  if  no  stars  were  ever  visible.  There  are,  therefore,  two  en- 
tirely distinct  ways  of  finding  when  the  sun  or  the  earth  has  completed 
its  apparent  circuit  around  the  celestial  sphere;  the  one  by  the  transit 
instrument  and  sidereal  clock,  which  show  when  the  sun  returns  to 
the  same  position  among  tlte  stars,  the  other  by  the  measurement  of 
altitude,  which  shows  when  it  returns  to  the  same  e</uin<u:  By  the 
former  method,  already  described,  we  conclude  that  it  has  completed 
an  annual  circuit  when  it  returns  to  the  same  star;  by  the  latter  when 
it  returns  to  the  same  equinox.  These  two  methods  will  give  slightly 
different  results  for  the  length  of  the  year,  for  a  reason  to  be  here- 
after described. 

The  Zodiac  and  its  Divisions. — The  zodiac  is  a  belt  in  the  heavens, 
commonly  considered  as  extending  some  8°  on  each  side  of  the 
ecliptic,  and  therefore  about  16°  wide.  The  planets  known  to  the 
ancients  are  always  seen  within  this  belt.  At  a  very  early  day  the 
zodiac  was  mapped  out  into  twelve  signs  known  as  the  signs  of  the 
zodiac,  the  names  of  which  have  been  handed  down  to  the  present 
time.  Each  of  these  signs  was  supposed  to  be  the  seat  of  a  constella- 
tion after  which  it  was  called.  Commencing  at  the  vernal  equinox, 
the  first  thirty  degrees  through  which  the  sun  passed,  or  the  region 
among  the  stars  in  which  it  was  found  during  the  month  following, 
was  called  the  sign  Aries.  The  next  thirty  degrees  was  called 
Taurus.  The  names  of  all  the  twelve  signs  in  their  proper  order, 
with  the  approximate  time  of  the  sun's  entering  upon  each,  are  as 
follows: 

Aries,  the  Ram,  March  20. 

Taurus,  the  Bull,  April  20. 

Gemini,  the  Twins,  May  20. 

Cancer,  the  Crab,  June  21. 

Leo,  the  Lion,  July  22. 

Virgo,  the  Virgin,  August  22. 

Libra,  the  Balance,  September  22. 

Scorpius,  the  Scorpion,  October  23. 

Sagittarius,  the  Archer,  November  23. 

Capricornus,  the  Goat,  December  21. 

Aquarius,  the  Water-bearer,         January  20. 

Pisces,  the  Fishes,  February  19. 


MOTIONS  OF  THE  EAHT1L  91 

Each  of  these  signs  coincides  roughly  with  a  constellation  in  the 
heavens;  and  thus  there  are  twelve  constellations  called  by  the 
names  of  these  signs,  but  the  signs  and  the  constellations  no  longer 
correspond.  Although  the  sun  now  crosses  the  equator  and  enters 
the  sign  Aries  on  the  20th  of  March,  he  does  not  reach  the  constella- 
tion Aries  until  nearly  a  month  later.  This  arises  from  the  preces- 
sion of  the  equinoxes,  to  be  explained  hereafter. 

OBLIQUITY  OF  THE  ECLIPTIC. 

We  have  already  stated  that  when  the  sun  is  at  the  sum- 
mer solstice  it  is  about  23£°  north  of  the  equator,  and  when 
at  the  winter  solstice,  about  23$°  south.  This  shows  that 
the  ecliptic  and  equator  make  an  angle  of  about  23|°  with 
each  other.  This  angle  is  called  the  obliquity  of  the  eclip- 
tic, and  its  determination  is  very  simple.  It  is  only  neces- 
sary to  find  by  repeated  observation  the  sun's  greatest  north 
declination  at  the  summer  solstice,  and  its  greatest  south 
declination  at  the  winter  solstice.  Either  of  these  declina- 
tions, which  must  be  equal  if  the  observations  are  accurate- 
ly made,  will  give  the  obliquity  of  the  ecliptic.  It  has  been 
continually  diminishing  from  the  earliest  ages  at  a  rate  of 
about  half  a  second  a  year,  or,  more  exactly,  about  47*  in 
a  century.  This  diminution  is  due  to  the  gravitating 
forces  of  the  planets,  and  will  continue  for  several  thousand 
years  to  come.  It  will  not,  however,  go  on  indefinitely, 
but  the  obliquity  will  only  oscillate  between  comparatively 
narrow  limits. 

In  the  preceding  paragraphs  we  have  explained  the 
apparent  annual  circuit  of  the  sun  relative  to  the  equator, 
and  shown  how  the  seasons  are  related  to  this  course.  In 
order  that  the  student  may  clearly  grasp  the  entire  subject, 
it  is  necessary  to  show  the  relation  o2  these  apparent  move- 
ments to  the  actual  movement  of  the  earth  around  the 
sun. 


92  ASTRONOMY. 

To  understand  the  relation  of  the  equator  to  the  ecliptic,  we  must 
rememl>er  that  the  celestial  pole  and  the  celestial  equator  have  really 
no  reference  whatever  to  the  heavens,  but  depend  solely  on  the  direc- 
tion of  the  earth's  axis  of  rotation.*  The  pole  of  the  heavens  is  noth- 
ing more  than  that  point  of  the  celestial  sphere  toward  which  the 
earth's  axis  happens  to  point.  If  the  direction  of  this  axis  changes,  the 
position  of  the  celestial  pole  among  the  stars  will  change  also;  though 
to  an  observer  on  the  earth,  unconscious  of  the  change,  it  would 
seem  as  if  the  starry  sphere  moved  while  the  pole  remained  at  rest. 
Again,  the  celestial  equator  being  merely  the  great  circle  in  which 
the  plane  of  the  earth's  equator,  extended  out  to  infinity  in  every 
direction,  cuts  the  celestial  sphere,  any  change  in  the  direction  of  the 
pole  of  the  earth  would  necessarily  change  the  position  of  ihe  equator 
among  the  stars.  Now  the  positions  of  the  celestial  pole  and  the 
celestial  equator  among  the  stars  seem  to  remain  unchanged  through- 
out the  year.  (There  is,  indeed,  a  minute  change,  but  it  does  not 
affect  our  present  reasoning.)  This  shows  that,  as  the  earth  revolves 
around  the  sun,  its  axis  is  constantly  directed  toward  nearly  the 
same  point  of  the  celestial  sphere. 


THE  SEASONS. 

The  conclusions  to  which  we  are  thus  led  respecting  the 
real  revolution  of  the  earth  are  shown  in  Fig.  32.  Here  S 
represents  the  sun,  with  the  orbit  of  the  earth  surrounding  it, 
but  viewed  nearly  edgeways  so  as  to  be  much  foreshortened. 
A  B  CD  are  the  four  cardinal  positions  of  the  earth  which 
correspond  to  the  cardinal  points  of  the  apparent  path  of  the 
.sun  already  described.  In  each  figure  of  the  earth  N  S  is 
the  axis,  N  being  its  north  and  8  its  south  pole.  Since 
this  axis  points  in  the  same  direction  relative  to  the  stars 
during  an  entire  year,  it  follows  that  the  different  lines  N  S 
are  all  parallel.  Again,  since  the  equator  does  not  coincide 
with  the  ecliptic,  these  lines  are  not  perpendicular  to  the 
ecliptic,  but  are  inclined  from  this  perpendicular  by  23^°. 

When  the  earth  is  at  A  the  sun's  north-polar  distance  (the 

*  Just  as  the  horizon  and  zenith  depend  only  on  the  situation  of  the  observer. 


MOTIONS  OF  THE  EARTH. 


93 


angle  at  the  centre  of  the  earth  at  A  between  the  lines  to 
the  north  pole  and  to  the  sun)  is  113^°;  at  B  it  is  90°;  at 
G  it  is  66^°;  at  D  it  is  again  90°,  and  between  66£  and 
113^°  the  north-polar  distance  continually  varies.  This 
may  be  plainer  if  the  student  draws  the  lines  S A,  SB, 
SC9  SD,  and  prolongs  the  lines  N8  at  each  position  of 
the  earth. 

Now  the  sun  shines  on  only  one  half  of  the  earth;  viz., 
that  hemisphere  turned  toward  him.  This  hemisphere  is 
left  bright  in  each  of  the  figures  of  the  earth  at  A,  B,  0,  D. 


FIG.  32.— CAUSES  OF  THE  SEASONS. 

Consider  the  diagram  at  A,  and  remember  that  the  earth 
is  turning  round  so  that  every  observer  is  carried  round 
his  parallel  of  latitude  every  24  hours.  The  parallels  are 
drawn  in  the  cut,  and  it  is  plain  that  a  person  near  JVwill 
remain  in  darkness  all  the  24  hours  ;  any  one  in  the  north- 
ern hemisphere  is  less  than  half  the  time  in  the  light— that 
is,  the  sun  is  less  than  half  the  time  above  his  horizon — 
and  a  person  in  the  southern  hemisphere  is  more  than  half 
the  time  in  the  light.  At  the  equator  the  days  and  nights 


94  ASTRONOMY. 

are  always  equal.  At  the  south  pole  it  is  perpetual  day. 
The  spectator  near  the  south  pole  is  carried  round  in  a 
parallel  of  latitude  which  is  perpetually  shined  upon. 
This  is  the  winter  solstice  (midwinter  in  the  northern 
hemisphere,  midsummer  in  the  southern). 

Next  suppose  the  earth  at  B :  £  is  90°  from  A  ;  that  is, 
3  months  later.  The  sun's  rays  just  graze  the  north  and 
south  poles;  each  parallel  of  latitude  is  half  light  and  half 
dark  ;  the  days  and  nights  are  equal.  This  is  the  equinox 
of  spring — the  vernal  equinox.  The  sun's  north-polar  dis- 
tance is  90°.  At  C  we  have  the  *?/ninn'r  solstice  (summer 
in  the  northern  hemisphere,  winter  in  the  southern). 
Here  is  perpetual  day  at  the  north  pole,  perpetual  night  at 
the  south;  long  days  to  all  the  northern  hemisphere,  long 
nights  in  the  southern.  Three  months  later  we  have  the 
auhutnwt  equinox  at  D. 

This  change  of  the  seasons  depends  upon  the  change  of 
the  sun's  north-polar  distance. 

•The  exact  phenomena  at  each  place  may  be  studied  by 
constructing  a  diagram  for  the  latitude  of  that  place1  (sec 
page  42)  and  assuming  the  sun's  north-polar  distance  as 
follows : 

March  21,  N.P.D.     90°,  Vernal  Equinox. 

June  20,  N.P.D.     GG^,  Summer  Solstice. 

September  21,  N.P.D.     90,  Autumnal  Equinox. 

December  21,  N.P.D.  113J,  Winter  Solstice. 

Two  such  diagrams  are  given  in  the  text-book  (page  28). 
The  student  should  be  able  to  pro^e  that  the  sun  is  always 
in  the  zenith  of  some  place  in  the  torrid  zone. 


MOTIONS  OF  THE  EARTH.  95 


CELESTIAL  LATITUDE  AND  LONGITUDE. 

To  describe  the  positions  of  the  sun  and  planets  in  space 
we  need  two  new  co-ordinates. 

The  Celestial  Latitude  of  a  star  is  its  angular  distance 
north  or  south  of  the  ecliptic. 

The  Celestial  Longitude  of  a  star  is  its  angular  distance 
from  the  vernal  equinox  measured  on  the  ecliptic  from 
west  to  east.  Having  the  right  ascension  and  declination 
of  a  body  (which  can  be  had  by  observation),  we  can  com- 
pute its  celestial  latitude  and  longitude.  These  co-ordinates 
are  no  longer  observed  (as  they  were  by  the  ancients),  but 
deduced  from  observations  of  right  ascension  and  declina- 
tion. 


CHAPTER  V. 
THE  PLANETARY  MOTIONS. 

APPARENT  AND  REAL  MOTIONS  OF  THE  PLANETS. 

Definitions. — The  solar  system  comprises  a  number  of 
bodies  of  various  orders  of  magnitude  and  distance,  sub- 
jected to  many  complex  motions.  Our  attention  will  be 
particularly  directed  to  the  motions  of  the  great  planets. 
These  bodies  may,  with  respect  to  their  apparent  motions, 
be  divided  into  three  classes. 

Speaking,  for  the  present,  of  the  sun  as  a  planet,  the 
first  class  comprises  the  sun  and  moon.  We  have  seen  that 
if,  upon  a  star  chart,  we  mark  down  the  positions  of  the 
sun  day  by  day,  they  will  all  fall  into  a  regular  circle  which 
marks  out  the  ecliptic.  The  monthly  course  of  the  moon 
is  found  to  be  of  the  same  nature;  and  although  its  motion 
is  by  no  means  uniform  in  a  month,  it  is  always  toward  the 
east,  and  always  along  or  very  near  a  certain  great  circle. 

The  second  class  comprises  Venus  and  Mercury.  The 
apparent  motion  of  these  bodies  is  an  oscillating  one  on 
each  side  of  the  sun.  If  we  watch  for  the  appearance  of 
one  of  these  planets  after  sunset  from  evening  to  evening, 
we  shall  find  it  to  appear  above  the  western  horizon.  Night 
after  night  it  will  be  farther  and  farther  from  the  sun  until 
it  attains  a  certain  maximum  distance;  then  it  will  appear 
to  return  towards  the  sun  again,  and  for  a  while  to  be  lost 


THE  PLANETARY  MOTIONS.  97 

in  its  rays.  A  few  days  later  it  will  reappear  to  the  west 
of  the  sun,  and  thereafter  be  visible  in  the  eastern  horizon 
before  sunrise.  In  the  case  of  Mercury  the  time  required 
for  one  complete  oscillation  back  and  forth  is  about  four 
months;  and  in  the  case  of  Venus  it  is  more  than  a  year 
and  a  half. 

The  third  class  comprises  Mars,  Jupiter,  and  Saturn,  as 
well  as  a  great  number  of  planets  not  visible  to  the  naked 
eye.  The  general  or  average  motion  of  these  planets  is 
toward  the  east,  a  complete  revolution  in  the  celestial 
sphere  being  performed  in  times  ranging  from  two  years  in 
the  case  of  Mars  to  164  years  in  that  of  Neptune.  But, 
instead  of  moving  uniformly  forward,  they  seem  to  have  a 
swinging  motion;  first,  they  move  forward  or  toward  the 
east  through  a  pretty  long  arc,  then  backward  or  westward 
through  a  short  one,  then  forward  through  a  longer  one, 
etc.  It  is  by  the  excess  of  the  longer  arcs  over  the  shorter 
ones  that  the  circuit  of  the  heavens  is  made. 

The  general  motion  of  the  sun,  moon,  and  planets  among 
the  stars  being  toward  the  east,  motion  in  this  direction  is 
called  direct;  motions  toward  the  west  are  called  retrograde. 
During  the  periods  between  direct  and  retrograde  motion 
the  planets  will  for  a  short  time  appear  stationary. 

The  planets  Venus  and  Mercury  are  said  to  be  at  greatest 
elongation  when  at  their  greatest  angular  distance  from  the 
sun.  The  elongation  which  occurs  with  the  planet  east  of 
the  sun,  and  therefore  visible  in  the  western  horizon  after 
sunset,  is  called  the  eastern  elongation,  the  other  the  west- 
ern one. 

A  planet  is  said  to  be  in  conjunction  with  the  sun  when 
it  is  in  the  same  direction  as  seen  from  the  earth,  or  when, 
as  it  seems  to  pass  by  the  sun,  it  approaches  nearest  to  it. 


98  ASTRONOMY. 

It  is  said  to  be  in  opposition  to  the  sun  when  exactly  in  the 
opposite  direction — rising  when  the  sun  sets,  and  vice 
versa.*  If,  when  a  planet  is  in  conjunction,  it  is  between 
the  earth  and  the  sun,  the  conjunction  is  said  to  be  an 
inferior  one;  if  beyond  the  sun,  it  is  said  to  be  superior. 


FIG.  33.— ORBITS  OF  THE  PLANETS. 

Arrangements  and  Motions  of  the  Planets, — The  sun  is 
the  real  centre  of  the  solar  system,  and  the  planets  proper 
revolve  around  it  as  the  centre  of  motion.  The  order  of 
the  five  innermost  large  planets,  or  the  relative  position  of 

*  A  planet  is  in  conjunction  with  the  sun  when  it  has  the  same 
geocentric  longitude;  in  opposition  when  the  longitudes  differ  1$Q°. 


THE  PLANETARY  MOTIONS.  99 

their  orbits,  is  shown  in  Fig.  33.  These  orbits  are  all 
nearly,  but  not  exactly,  in  the  same  plane.  The  planets 
Mercury  and  Venus  which,  as  seen  from  the  earth,  never 
appear  to  recede  very  far  from  the  sun,  are  in  reality  those 
which  revolve  inside  the  orbit  of  the  earth.  The  planets 
of  the  third  class,  which  perform  their  circuits  at  all  dis- 
tances from  the  sun,  are  what  we  call  the  superior  planets, 
and  are  more  distant  from  the  sun  than  the  earth  is.  Of 
these  the  orbits  of  Mars,  Jupiter,  and  a  swarm  of  telescopic 
planets  are  shown  in  the  figure;  next  outside  of  Jupiter 
comes  Saturn,  the  farthest  planet  readily  visible  to  the 
naked  eye,  and  then  Uranus  and  Neptune,  telescopic  plan- 
ets. On  the  scale  of  Fig.  33  the  orbit  of  Neptune  would 
be  more  than  two  feet  in  diameter.  Finally,  the  moon  is 
a  small  planet  revolving  around  the  earth  as  its  centre,  and 
carried  with  the  latter  as  it  moves  around  the  sun. 

Inferior  planets  are  those  whose  orbits  lie  inside  that  of 
the  earth,  as  Mercury  and  Venus. 

Superior  planets  are  those  whose  orbits  lie  outside  that 
of  the  earth,  as  Mars,  Jupiter,  Saturn,  etc. 

The  farther  a  planet  is  situated  from  the  sun  the  slower 
is  its  orbital  motion.  Therefore,  as  we  go  from  the  sun, 
the  periods  of  revolution  are  longer,  for  the  double  reason 
that  the  planet  has  a  larger  orbit  to  describe  and  moves 
more  slowly  in  its  orbit.  It  is  to  this  slower  motion  of  the 
outer  planets  that  the  occasional  apparent  retrograde  mo- 
tion of  the  planets  is  due,  as  may  be  seen  by  studying  Fig. 
34.  The  apparent  position  of  a  planet,  as  seen  from  the 
earth,  is  determined  by  the  line  joining  the  earth  and 
planet.  Supposing  this  line  to  be  continued  so  as  to  inter- 
sect the  celestial  sphere,  the  apparent  motion  of  the  planet 
will  be  defined  by  the  motion  of  the  point  in  which  the  line 


100 


ASTRONOMY. 


intersects  the  sphere.     If  this  motion  is  toward  the  east,  it 
is  direct ;  if  toward  the  west,  retrograde. 

The  Apparent  Motion  of  a  Superior  Planet.— In  the  figure 
let  S  be  the  sun,  ABCDEF  the  orbit  of  the  earth,  and 
HIKLMN  the  orbit  of  a  superior  planet,  as  Mars. 
When  the  earth  is  at  A  suppose  Mars  to  be  at  H,  and  let 
B  and  /,  C  and  K,  D  and  L,  E  and  M,  F  and  N  be  corre- 
sponding positions.  As  the  earth  moves  faster  than  Mars 


FIG 


the  arcs  AB,  BC,  etc.,  correspond  to  greater  angles  at  the 
centre  than  H  I,  IK,  etc. 

When  the  earth  is  at  A,  Mars  will  be  seen  on  the  celestial 
sphere  at  the  apparent  position  0.  When  the  earth  is  at 
B,  Mars  will  be  seen  at  P.  As  the  earth  describes  AB, 
Mars  will  appear  to  describe  OP  moving  in  the  same  direc- 
tion as  the  earth's  orbital  motion;  i.e.,  direct.  When  tho 
earth  is  at  C,  Mars  is  at  K  (in  opposition  to  the  sun),  and 
its  motion  is  retrograde  along  the  small  arc  beyond  QP  in 


THE  PLANETARY  MOTIONS.  101 

the  figure.  When  the  earth  reaches  D  the  planet  has  fin- 
ished its  retrograde  arc.  As  the  earth  moves  from  D  to  E 
the  planet  moves  from  L  to  M,  and  the  lines  joining  earth 
and  planet  are  parallel  and  correspond  to  a  fixed  position 
on  the  celestial  sphere.  The  planet  is  at  a  station.  As  the 
earth  moves  from  E  to  F  the  apparent  motion  of  Mars  is 
direct  from  Q  to  R;  and  in  the  same  way  the  apparent 
motion  of  any  outer  planet  can  be  determined  by  drawing 
its  orbit  outside  of  the  earth's  orbifc  ABODE Fsn\d  laying 
off  on  this  orbit  positions  which  correspond  to  the  points 
ABCD EF  and  joining  the  corresponding  positions.  It 
will  be  found  that  all  outer  planets  have  a  retrograde  mo- 
tion at  opposition,  etc. 

The  Apparent  Motion  of  an  Inferior  Planet.— To  deter- 
mine the  corresponding  phenomena  for  an  inferior  planet 
the  same  figure  maybe  used.  Suppose  HIKL  M  to  be 
the  orbit  of  the  earth,  and  A  B  C D  E F  t\\Q  orbit  of  Mer- 
cury, and  suppose  H  and  A,  I  and  B,  etc.,  to  be  corre- 
sponding positions.  Suppose  H  A  to  be  tangent  to  Mer- 
cury's orbit.  The  angle  A  H  S  is  the  elongation  of  Mer- 
cury, and  it  is  the  greatest  elongation  it  can  ever  have. 

Let  the  student  construct  the  apparent  positions  of  Mer- 
cury as  seen  from  the  earth  from  the  data  given  in  the 
figure.  From  the  apparent  positions  he  can  determine  the 
apparent  motions.  As  Mercury  moves  from  A  B  its  ap- 
parent motion  is  direct.  On  both  sides  of  the  inferior  con- 
junction C  its  motion  is  retrograde.  From  D  to  E  it  is 
stationary.  Also  let  him  construct  the  apparent  positions 
of  the  sun  at  different  times  by  drawing  the  linos  H  S,  IS, 
K S,  etc.,  towards  the  right.  The  angles  between  the  ap- 
parent positions  of  Mercury  and  the  sun  will  be  the  elonga- 
tions of  Mercury  at  various  times. 


102  ASTRONOMY. 

Theory  of  Epicycles.— Complicated  as  the  apparent  motions  of  the 
planets  were,  it  was  seen  by  the  ancient  astronomers  that  they  could 
be  represented  by  a  combination  of  two  motions.  First,  a  small  circle 
or  epicycle  was  supposed  to  move  around  tlie  earth  (not  the  sun) 
with  a  regular,  though  not  uniform,  forward  motion,  and  then  the 
planet  was  supposed  to  move  around  the  circumference  of  this  circle. 
The  relation  of  this  theory  to  the  true  one  was  this:  The  regular 
forward  motion  of  the  epicycle  represents  the  real  motion  of  the 
planet  around  the  sun,  while  the  motion  of  the  planet  around  the 
circumference  of  the  epicycle  is  an  apparent  one  arising  from  the 

revolution  of  the  eurth  around  the 
sun.  To  explain  this  we  must  under- 
stand some  of  the  laws  of  relative  mo- 
tion. 

It  is  familiarly  known  that  if  an 
observer  in  unconscious  motion  looks 
upon  an  object  ait  rest,  the  object  will 
appear  to  him  to  move  in  a  direction 
opposite  that  in  which  he  moves.  As 
a  result  of  this  law,  if  the  observer  is 
uncon.-ciously  describing  a  circle,  an 
object  at  rest  will  appear  to  him  to 
describe  a  circle  of  equal  si/e.  This 
is  shown  by  the  following  figure.  Let 
<S  represent  the  sun,  and  ADCDEF 
the  orbit  of  the  earth.  Let  us  sup- 
pose the  observer  on  the  earth  carried 
around  in  this  orbit,  but  imagining 
himself  at  rest  at  S,  the  centre  of  mo- 
tion. Suppose  he  keeps  observing  the 
direction  and  distance  of  the  planet  P, 
which  for  the  present  we  suppose  to 
be  at  rest,  since  it  is  only  the  relative 
motion  that  we  shall  have  to  consider. 
When  the  observer  is  at  A  he  really 

sees  the  planet  in  a  direction  and  distance  AP,  but  imagining  himself 
at  S  he  thinks  he  sees  the  planet  at  the  point  a  determined  by  drawing 
a  line  Sa  parallel  and  equal  to  A  P.  As  he  passes  from  A  to  B  the 
planet  will  seem  to  him  to  move  in  the  opposite  direction  from  a  to 
b,  the  point  b  being  determined  by  drawing  S  b  equal  and  parallel 
to  BP.  As  he  recedes  from  the  planet  through  the  arc  BCD,  the 
planet  seems  to  recede  from  him  through  b  c  d;  and  while  he  moves 
from  left  to  right  through  DE  the  planet  seems  to  move  from  right 


PLANKTAET  MOTTONS.  103 

to  left  through  de.  Finally,  as  he  approaches  the  planet  through 
the  arc  E FA  the  planet  seems  to  approach  him  through  efa,  and 
when  he  returns  to  A  the  planet  will  appear  at  a,  as  in  the  begin- 
ning. Thus  the  planet,  though  really  at  rest,  would  seem  to  him  to 
move  over  the  circle  abcdef  corresponding  to  that  in  which  the 
observer  himself  was  carried  around  the  sun. 

The  planet  being  really  in  motion,  it  is  evident  that  the  combined 
effect  of  the  real  motion  of  the  planet  and  the  apparent  motion 
around  the  circle  abcdef  will  be  represented  by  carrying  the  centre 
of  this  circle  P  along  the  true  orbit  of  the  planet.  The  motion  of 
the  earth  being  more  rapid  than  that  of  an  outer  planet,  it  follows 
that  the  apparent  motion  of  the  planet  through  a  b  is  more  rapid 
than  the  real  motion  of  P  along  the  orbit.  Hence  in  this  part  of  the 
orbit  the  movement  of  the  planet  will  be  retrograde.  In  every  other 
part  it  will  be  direct,  because  the  progressive  motion  of  P  will  at 
least  overcome,  sometimes  be  added  to,  the  apparent  motion  around 
the  circle. 

In  the  ancient  astronomy  the  apparent  small  circle  abcdef  was 
called  the  epicycle. 

In  the  case  of  the  inner  planets  Mercury  and  Venus  the  relation  of 
the  epicycle  to  the  true  orbit  is  reversed.  Here  the  epicyclic  motion 
is  that  of  the  planet  round  its  real  orbit;  that  is,  the  true  orbit  of  the 
planet  around  the  sun  was  itself  taken  for  the  epicycle,  while  the 
forward  motion  was  really  due  to  the  apparent  revolution  of  the  sun 
produced  by  the  annual  motion  of  the  earth. 

In  Fig.  29  the  sun  would  successively  appear  to  be  at  1',  2',  3',  4', 
5',  and  at  each  of  these  points  the  inferior  planet  would  really  revolve 
about  1',  2',  3',  4',  5'. 

Although  the  observations  of  two  thousand  years  ago 
could  be  tolerably  well  explained  by  these  epicycles,  yet 
with  every  increase  of  accuracy  in  observation  new  compli- 
cations had  to  be  introduced,  until  at  the  time  of  COPER- 
NICUS (1542)  the  confusion  was  very  great. 

The  Copernican  System  of  the  World,— COPERNICUS  re- 
vived a  belief  taught  by  some  of  the  ancients  that  the  sun 
was  the  centre  of  the  system,  and  that  the  earth  and  plan- 
ets moved  about  him  in  circular  orbits.  While  this  was  a 
step,  and  a  great  step,  forward,  purely  circular  orbits  for 
the  planets  would  not  explain  all  the  facts. 


104  ASTRONOMY. 

From  the  time  of  COPERNICUS  (1542)  till  that  of  KEP- 
LER and  GALILEO  (1600  to  1630)  the  whole  question  of  the 
true  system  of  the  universe  was  in  debate.  The  circular 
orbits  introduced  by  COPERNICUS  also  required  a  complex 
system  of  epicycles  to  account  for  some  of  the  observed 
motions  of  the  planets,  and  with  every  increase  in  accuracy 
of  observation  new  devices  had  to  be  introduced  into  the* 
system  to  account  for  the  new  phenomena  observed.  In 
short,  the  system  of  COPERNICUS  accounted  for  so  many 
facts  (as  the  stations  and  retrogradations  of  the  planets) 
that  it  could  not  be  rejected,  and  had  so  many  difficulties 
that  without  modification  it  could  not  be  accepted. 

KEPLER'S  LAWS  OF  PLANETARY  MOTION. 

Kepler  and  Galileo.— KEPLER  (born  1571,  d.  1630)  was 
ii  genius  of  the  first  order.  He  had  a  thorough  acquaint- 
ance with  the  old  systems  of  astronomy  and  a  thorough  be- 
lief in  the  essential  accuracy  of  the  Copernican  system, 
whose  fundamental  theorem  was  that  the  sun  and  not  the 
earth  was  the  centre  of  our  system.  He  lived  nt  the  same 
time  with  GALILEO,  who  was  the  first  person  to  observe  the 
heavenly  bodies  with  a  telescope  of  his  own  invention,  and 
he  had  the  benefit  of  accurate  observations  of  the  planets 
made  by  TYCHO  BRAKE.  The  opportunity  for  determin- 
ing the  true  laws  of  the  motions  of  the  planets  existed  then 
as  it  never  had  before;  and  fortunately  he  was  able, 
through  labors  of  which  it  is  difficult  to  form  an  idea  to- 
day, to  reach  a  true  solution. 

The  Periodic  Time  of  a  Planet.— The  time  of  revolution 
of  a  planet  in  its  orbit  round  the  sun  (its  periodic  time) 
can  be  learned  by  continuous  observations  of  the  planet's 
course  among  the  stars. 


THE  PLANETARY  MOTIONS.  105 

From  ancient  times  the  geocentric  positions  of  the 
planets  had  been  observed.  These  positions  were  referred 
to  the  places  of  the  brightest  fixed  stars,  and  the  relative 
places  of  these  stars  had  been  fixed  with  a  tolerable  ac- 
curacy. The  time  required  for  a  planet  to  move  from  one 
star  to  the  same  star  again  was  the  time  of  revolution  of 
the  planet  referred  to  the  earth. 

The  real  motion  of  the  earth  was  known  from  observa- 
tions of  the  apparent  motion  of  the  sun.  By  calculation 
it  was  possible  to  refer  the  motions  as  observed  (i.e.,  with 
reference  to  the  earth)  to  the  real  motions  (i.e.,  those  about 
the  sun). 

It  was  thus  found  that  the  periodic  times  of  the  known 
planets  were: 


For  Mercury  about     88  days. 
Venus          "      225     " 
Earth          "      365     " 


For  Mars    about       687  days 
Jupiter     "       4,333     " 
Saturn     "     10,759     " 


These  values  were  known  to  the  predecessors  of  COPER- 
KICUS.  He  also  showed  (what  is  evident  when  we  examine 
Fig.  34)  that  to  an  observer  on  the  sun  the  motions  of 
the  planets  would  be  always  direct,  and  that  no  stations  or 
retrogradations  of  the  planets  would  be  seen  from  the  sun. 

We  may  determine  the  relative  distances  of  a  planet  and 
the  sun  from  each  other  by  the  method  illustrated  in  Fig. 
36.  8  is  the  sun,  E  the  earth,  and  M  the  planet  when  the 
planet  is  in  opposition  to  the  sun.  The  time  at  which  the 
planet  is  in  opposition  is  known  by  noting  the  date  when  it 
is  on  the  meridian  at  midnight.  After  a  certain  period, 
say  one  hundred  days,  the  planet  will  have  moved  to  M' 
and  the  earth  to  E' .  Since  we  know  the  periodic  times 
of  the  earth  and  planet,  we  can  calculate  the  angles  M'  8  M 


106  ASTRONOMY. 

and  E'  S  E  which  the  planet  and  earth  will  move  over  in 
any  interval. 

At  this  date  we  can  observe  the  angle  M'  E'  S,  which  is 
the  angular  distance  between  the  sun  and  planet.  (This 
is  called  the  planet's  elongation.) 

In  the  triangle  M' S  E'  we  shall  know  the  angle  at  E', 
by  observation,  the  angle  at  S,  since  it  is  the  difference 
between  the  known  angles  E  S  E'  and  M  S  M',  and  hence 


FIG.  36. 

the  angle  at  M' .  Therefore  a  triangle  can  be  constructed 
which  has  the  same  shape  as  M*  S  E',  and  the  relative 
length  of  S  M'  and  S  E'  thus  becomes  known. 

Nothing  is  known  from  this  calculation  of  the  absolute 
values  of  S  E  or  S  Mm  miles,  but  observations  of  this  sort 
on  all  the  planets  give  their  relative  distances  from  the 
sun.  If  we  call  8  E  the  astronomical  unit,  it  was  known 
to  the  ancients  that 


PLANETARY  MOTIONSt**          107 

For  Mercury  ^  =  0.3871 
Venus  a*  =  0.7233 
Earth  a3  =  1.0000 
Jfors  a4  =  1.5237 
Jupiter  a6  =  5.2028 
=  9.5388 


The  calculation  which  we  have  described  could  be  made 
for  every  position  of  each  planet,  and  thus  its  distances  from 
the  sun  at  every  point  of  its  orbit  could  be  determined. 

The  radius-  vector  of  a  planet  is  the  line  which  joins  it  to 
the  sun. 

The  relative  lengths  of  the  radii-vectores  of  each  planet 
at  any  time  were  thus  found  by  observation,  in  terms  of 
the  earth's  radius-vector  =  1. 


FIG.  37. 

Suppose  Sto  be  the  sun,  and  draw  lines  SP,  SPl9 
S Pn,  etc.,  to  the  heliocentric  positions  of  a  planet  at  dif- 
ferent times.  On  these  lines  lay  off  distances  SP,  SPl9 
S P9,  etc.,  proportional  to  the  lengths  of  the  planet's  radii- 
vectores  determined  as  above.  Join  the  points  P,  Pl9  P9, 
P,,  etc.  The  line  joining  these  is  a  visible  representation 


108  ASTRONOMY. 

of  the  shape  of  the  planet's  orbit,  drawn  to  scale.  This 
shape  is  not  that  of  a  circle,  but  it  is  an  ellipse,  and  the 
sun,  8,  is  not  at  the  centre  but  at  a  focus  of  the  ellipse. 

An  ellipse  is  a  curve  such  that  the  sum  of  the  distances 
of  every  point  of  the  curve  from  two  fixed  points  (the  foci) 
is  a  constant  quantity. 


Fio.  88 

The  Ellipse.—  A  D  tf  P  is  an  ellipse  ;  S  and  Sf  are  the  foci.  By  the 
definition  of  an  ellipse  SP-\-P8=  A  C,  and  this  is  true  for  every 
point.  S  is  the  focus  occupied  by  the  sun,  "  the  filled  focus."  A  S 
is  the  least  distance  of  the  planet  from  the  sun,  its  perihelion  distance; 
and  A  is  the  perihelion,  that  point  nearest  the  sun.  C  is  the  aphelion, 
the  point  farthest  from  the  sun.  8  A,  SD,  SC,  SB,  SP  are  radii- 
vectores  at  different  parts  of  the  orbit.  A  C  is  the  major  axis 
of  the  orbit  =  2a.  This  major  axis  of  the  orbit  is  twice  the  mean 
distance  of  the  planet  from  the  sun,  a.  BD  is  the  minor  axis,  26. 
The  ratio  of  08  to  OA  is  the  eccentricity  of  the  ellipse.  By  the 
definition  of  the  ellipse,  again,  BS+BS'=  A  C;  and  B8  =  BS=  a. 


S3,  or  08=  4/a*-^  and  the  eccentricity  of  the 

.OS     Vtf^V 
ellipse  is  _=__. 

Kepler's  Laws.  —  By  computations  based  on  the  observa- 
tions of  Mars  made  by  TYCHO  BRAHE,  KEPLER  deduced 


THE  PLANETAHY  MOTIONS.  109 

his  first  two  laws  of  motion  in  the  solar  system.  The  first 
law  of  KEPLER  is  — 

/.  Each  planet  moves  around  the  sun  in  an  ellipse,  hav- 
ing the  sun  at  one  of  its  foci.  To  understand  Law  II: 

Suppose  the  planet  to  be  at  the  points  P,  Pl9  P,,  P,,  P4, 
etc.,  at  the  times  T,  Tlt  T^  Tt,  T4,  etc.  (Fig.  37). 

Suppose  the  times  T^-  T,  T3-  Tt,  T6-  T4  to  be  equal. 
KEPLER  computed  the  areas  of  the  surfaces  P  8  Piy  Pa  $P3, 
P4SP6  and  found  that  these  areas  were  equal  also,  and 
that  this  was  true  for  each  planet.  The  second  law  of  KEP- 
LER is  — 

//.  The  radius-vector  of  each  planet  describes  equal  areas 
in  equal  times. 

These  two  laws  are  true  for  each  planet  moving  in  its 
own  ellipse  about  the  sun. 

For  a  long  time  KEPLER  sought  for  some  law  which 
should  connect  the  motion  of  one  planet  in  its  ellipse  with 
the  motion  of  another  planet  in  its  ellipse.  Finally  he 
found  such  a  relation  between  the  mean  distances  of  the 
different  planets  (see  table  on  page  107)  and  their  periodic 
times  (see  table  on  p.  105). 

His  third  law  is: 

///.  The  squares  of  the  periodic  times  of  the  planets  are 
proportional  to  the  cubes  of  their  mean  distances  from  the 
sun. 

That  is,  if  Tlt  T^  T3,  etc.,  are  the  periodic  times  of  the 
different  planets  whose  mean  distances  are  al9  #„  «s,  etc., 
then 


etc.  etc. 


110  ASTRONOMY. 

If  Tt  and  0,  are  the  periodic  time  and  the  mean  distance 
of  the  earth,  and  if  Tt  (=  1  year)  is  taken  as  the  unit  of 
time  and  a,  as  the  unit  of  distance,  then  we  shall  have 


and  so  on. 

The  data  which  KEPLER  had  were  not  quite  so  accurate 
as  those  which  we  have  given,  and  the  table  below  shows 
the  very  figures  on  which  KEPLER'S  conclusion  was  based: 

PLANET.                                    fll                          T  T  '-=-  O\ 
Mercury  ..............     0.2378             0.2408  years      1.013 

Venus  ................     0.6104             0.6151  1.008 

Earth  ................     1.0000             1.0000  1.000 

Mars  .................     1.8740             1.8810  1.004 

Jupiter  ...............  11.914  11.8764  0.996 

Saturn  ...............  28.058  29.4605  1.050 

Although  the  numbers  in  the  third  column  were  not 
strictly  the  same,  their  differences  were  no  greater  than 
might  easily  have  been  produced  by  the  errors  of  the  obser- 
vations which   KEPLER  used;  and  on  the  evidence  here 
given  he  advanced  his  third  law.     The  order  of  discovery 
of  the  true  theory  of  the  solar  system  was,  then  — 
I.  To  prove  that  the  earth  moved  in  space; 
II.  To  prove  that  the  centre  of  this  motion  was  the  sun; 

III.  To  establish  the  three  laws  of  KEPLER,  which  gave 
the  circumstances  of  this  motion. 

By  means  of  the  first  two  laws  of  KEPLER  the  motions  of  each 
planet  in  its  own  ellipse  became  known;  that  is,  the  position  of  the 
planet  at  any  future  time  could  be  predicted.  For  example,  if  the 
planet  was  at  P  at  a  time  7,  and  the  question  was  as  to  its  place  at  a 
subsequent  time  T,  this  could  be  solved  by  computing,  first,  how 


THE  PLANETARY  MOTIONS.  HI 

large  an  area  would  be  described  by  the  radius-vector  in  the  interval 
T  —  T  ;  and  second,  what  the  angle  at  8  of  the  sector  having  this 
area  would  be.  Then  drawing  a  line  through  S  making  this  angle 
with  the  line  £P(say  SP,),  and  laying  off  the  length  of  the  radius- 
vector  S P,,  the  position  of  the  planet  became  known. 

From  the  third  law  the  relative  values  of  the  mean  distances 
ai,  ay,  a4,  a6,  etc.,  could  be  determined  with  great  and  increasing  ac- 
curacy. 

T 

From  the  equation—  =  1,  a  could  be  determined  so  soon  as  I7 was 

known.  With  each  revolution  of  the  planet  T  became  known  more 
accurately,  as  did  also  a. 

These  laws  are  the  foundations  of  our  present  theory  of  the  solar 
system.  They  were  based  on  observation  pure  and  simple.  We  may 
anticipate  a  little  to  say  that  these  laws  have  been  compared  with 
the  most  precise  observations  we  can  m;ike  at  the  present  time,  and 
discussed  in  all  their  consequences  by  processes  unknown  to  KEP- 
LER, and  that  they  are  strictly  true  if  we  make  the  following  modifi- 
cations. 

If  there  were  only  one  planet  revolving  about  the  sun,  then  it 
would  revolve  in  a  perfect  ellipse,  and  obey  the  second  law  exactly. 
In  a  system  composed  of  the  sun  and  more  than  one  planet  each 
planet  disturbs  the  motion  of  every  other  slightly,  by  attracting  it 
from  the  orbit  which  it  would  otherwise  follow. 

Thus  neither  the  first  nor  the  second  law  can  be  precisely  true  of 
any  planet,  although  they  are  very  nearly  so.  In  the  same  way  the 
relation  between  the  orbits  of  any  two  planets  as  expressed  in  the 
third  law  is  not  precise,  although  it  is  a  very  close  approximation. 

Elements  of  a  Planet's  Orbit. — When  we  know  a  and  b  for  any  orbit, 
the  shape  and  size  of  the  orbit  is  known. 

Knowing  a  we  also  know  T,  the  periodic  time;  in  fact  a  is  found 
from  I  by  KEPLETC'S  law  III. 

If  we  know  the  planet's  celestial  longitude  (L)  at  a  given  epoch, 
say  December  31st,  1850,  we  have  all  the  elements  necessary  for 
finding  the  place  of  the  planet  in  its  orbit  at  any  time,  as  has  been 
explained  (page  110). 

The  orbit  lies  in  a  certain  plane;  this  plane  intersects  the  plane  of 
the  ecliptic  at  a  certain  angle,  which  we  call  the  inclination  i.  Know- 
ing i,  the  plane  of  the  planet's  orbit  is  fixed.  The  plane  of  the 
orbit  intersects  the  plane  of  the  ecliptic  in  a  line,  the  line  of  the  nodes. 
Half  of  the  planet's  orbit  lies  below  (south  of)  the  plane  of  the 
ecliptic  and  half  above.  As  the  planet  moves  in  its  orbit  it  must 
pass  through  the  plane  of  the  ecliptic  twice  for  every  revolution. 


112  ASTRONOMY. 

The  point  where  it  passes  through  the  ecliptic  going  from  the  south 
half  to  the  north  half  of  its  orbit  is  the  ascending  node;  the  point 
where  it  passes  through  the  ecliptic  going  from  north  to  south  is 
the  descending  node  of  the  planet's  orbit.  If  we  have  only  the  in- 
clination given,  the  orbit  of  the  planet  may  lie  anywhere  in  the  plane 
whose  angle  with  the  ecliptic  is  t.  If  we  fix  the  place  of  the  nodes, 
or  of  one  of  them,  the  orbit  is  thus  fixed  in  its  plane.  This  we  do 
by  giving  the  (celestial)  longitude  of  the  ascending  node/}. 

Now  everything  is  known  except  the  relation  of  the  planet's  orbit 
to  the  sun.  This  is  fixed  by  the  longitude  of  t/ie  perilielion,  or  P. 

Thus  the  elements  of  a  planet's  orbit  are: 

i,  the  inclination  to  the  ecliptic,  which  fixes  the  plane  of  the  planet's 
orbit; 

fi,,  the  longitude  of  the  node,  which  fixes  the  position  of  the  line  of 
intersection  of  the  orbit  and  the  ecliptic; 

P,  the  longitude  of  the  perihelion,  which  fixes  the  position  of  the 
major  axis  of  the  planet's  orbit  with  relation  to  the  sun,  and  hence 
in  space; 

a  and  e,  the  mean  distance  and  eccentricity  of  the  orbit,  which  fix 
the  shape  and  size  of  the  orbit; 

2  and  M,  the  periodic  time  and  the  longitude  at  epoch,  which  enable 
the  place  of  the  planet  in  its  orbit,  and  hence  in  space,  to  be  fixed  at 
any  future  or  past  time. 

The  elements  of  the  older  planets  of  the  solar  system  are  now 
known  with  great  accuracy,  and  their  positions  for  two  or  three  cen- 
turies past  or  future  can  be  predicted  with  a  close  approximation  to  the 
accuracy  with  which  these  positions  can  be  observed. 


CHAPTER  VI. 
UNIVERSAL    GRAVITATION. 

NEWTON'S  LAWS  OF  MOTION 

THE  establishment  of  the  theory  of  universal  gravitation 
furnishes  one  of  the  best  examples  of  scientific  method 
which  is  to  be  found.  We  shall  describe  its  leading  features, 
less  for  the  purpose  of  making  known  to  the  reader  the 
technical  nature  of  the  process  than  for  illustrating  the 
true  theory  of  scientific  investigation,  and  showing  that  such 
investigation  has  for  its  object  the  discovery  of  what  we 
may  call  generalized  facts.  The  real  test  of  progress  is 
found  in  our  constantly  increased  ability  to  foresee  either 
the  course  of  nature  or  the  effects  of  any  accidental  or  arti- 
ficial combination  of  causes.  So  long  as  prediction  is  not 
possible,  the  desires  of  the  investigator  remain  unsatisfied. 
When  certainty  of  prediction  is  once  attained,  and  the 
laws  on  which  the  prediction  is  founded  are  stated  in  their 
simplest  form,  the  work  of  science  is  complete. 

To  the  pre-Newtonian  astronomers  the  phenomena  of 
the  geometrical  laws  of  planetary  motion,  which  we  have 
just  described,  formed  a  group  of  facts  having  no  connection 
with  anything  on  the  earth's  surface.  The  epicycles  of 
HIPPARCHUS  and  PTOLEMY  were  a  truly  scientific  concep- 
tion, in  that  they  explained  the  seemingly  erratic  motions 
of  the  planets  by  a  single  simple  law.  In  the  heliocentric 


114  ASTRONOMY. 

theory  of  COPERNICUS  this  law  was  still  further  simplified 
by  dispensing  in  great  part  with  the  epicycle,  and  replacing 
the  latter  by  a  motion  of  the  earth  around  the  sun,  of  the 
same  nature  with  the  motions  of  the  planets.  But  COPER- 
NICUS had  no  way  of  accounting  for,  or  even  of  describing 
with  rigorous  accuracy,  the  small  deviations  in  the  motions 
of  the  planets  around  the  sun.  In  this  respect  he  made  no 
real  advance  upon  the  ideas  of  the  ancients. 

KEPLER,  in  his  discoveries,  made  a  great  advance  in  rep- 
resenting the  motions  of  all  the  planets  by  a  single  set  of 
simple  and  easily  understood  geometrical  laws.  Had  the 
planets  followed  his  laws  exactly,  the  theory  of  planetary 
motion  would  have  been  substantially  complete.  Still, 
further  progress  was  desired  for  two  reasons.  In  the  first 
place,  the  laws  of  KEPLER  did  not  perfectly  represent  all 
the  planetary  motions.  When  observations  of  the  greatest 
accuracy  were  made,  it  was  found  that  the  planets  deviated 
by  small  amounts  from  the  ellipse  of  KEPLER.  Some  small 
emendations  to  the  motions  computed  on  the  elliptic  theory 
were  therefore  necessary.  Had  this  requirement  been  ful- 
filled, still  another  step  would  have  been  desirable;  namely, 
that  of  connecting  the  motions  of  the  planets  with  motions 
upon  the  earth,  and  reducing  them  to  the  same  laws. 

Notwithstanding  the  great  step  which  KEPLER  made  in 
describing  the  celestial  motions,  he  unveiled  none  of  the 
great  mystery  in  which  they  were  enshrouded.  When  KEP- 
LER said  that  observation  showed  the  law  of  planetary  mo- 
tion to  be  that  around  the  circumference  of  an  ellipse,  as 
asserted  in  his  law,  he  said  all  that  it  seemed  possible  to 
learn,  supposing  the  statement  perfectly  exact.  And  it 
was  all  that  could  be  learned  from  the  mere  study  of  the 
planetary  motions.  In  order  to  connect  these  motions  with 


UNIVERSAL   GRAVITATION.  115 

those  on  the  earth,  the  next  step  was  to  study  the  laws  of 
force  and  motion  here  around  us.  Singular  though  it  may 
appear,  the  ideas  of  the  ancients  on  this  subject  were  far 
more  erroneous  than  their  conceptions  of  the  motions  of 
the  planets.  We  might  almost  say  that  before  the  time  of 
GALILEO  scarcely  a  single  correct  idea  of  the  laws  of  motion 
was  generally  entertained  by  men  of  learning.  Among 
those  who,  before  the  time  of  NEWTON,  prepared  the  way 
for  the  theory  in  question,  GALILEO,  HUYGHENS,  and 
HOOKE  are  entitled  to  especial  mention.  The  general  laws 
of  motion  laid  down  by  NEWTON  were  three  in  number. 

Law  First:  Every  body  preserves  its  state  of  rest  or  of 
uniform  motion  in  a  right  line,  unless  it  is  compelled  to 
change  that  state  by  forces  impressed  thereon. 

It  was  formerly  supposed  that  a  body  acted  on  by  no  force  tended 
to  come  to  rest.  Here  lay  one  of  the  greatest  difficulties  which  the 
predecessors  of  NEWTON  fouud,  in  accounting  for  the  motion  of  the 
planets.  The  idea  that  the  sun  in  some  way  caused  these  motions 
was  entertained  from  the  earliest  times.  Even  PTOLEMY  had  a  vague 
idea  of  a  force  which  was  always  directed  toward  the  centre  of  the 
earth,  or,  which  was  to  him  the  same  thing,  toward  the  centre  of  the 
universe,  and  which  not  only  caused  heavy  bodies  to  fall,  but  bound 
the  whole  universe  together.  KEPLER,  again,  distinctly  affirms  the 
existence  of  a  gravitating  force  by  which  the  sun  acts  on  the  planets; 
but  he  supposed  that  the  sun  must  also  exercise  an  impulsive  forward 
force  to  keep  the  planets  in  motion.  The  reason  of  this  incorrect 
idea  was,  of  course,  that  all  bodies  in  motion  on  the  surface  of  the 
earth  had  practically  come  to  rest.  But  what  was  not  clearly  seen 
before  the  time  of  NEWTON,  or  at  least  before  GALILEO,  was  that 
this  arose  from  the  inevitable  resisting  forces  which  act  upon  all 
moving  bodies  upon  the  earth. 

Law  Second:  TJie  alteration  of  motion  is  ever  propor- 
tional to  the  moving  force  impressed)  and  is  made  in  the 
direction  of  the  right  line  in  which  that  force  acts. 


116  ASTRONOMY. 

The  first  law  might  be  considered  as  a  particular  case  of  this  sec- 
ond one  which  arises  when  the  force  is  supposed  to  vanish.  The  ac- 
curacy of  both  laws  can  be  proved  only  by  very  carefully  conducted 
experiments.  They  are  now  considered  as  conclusively  proved. 

Law  Third:  To  every  action  there  is  always  opposed  an 
equal  reaction  ;  or  the  mutual  actions  of  two  bodies  upon 
each  other  are  always  equal,  and  in  opposite  directions. 

That  is,  if  a  body  A  acts  in  any  way  upon  a  body  B,  B  will  exert 
a  force  exactly  equal  on  A  in  the  opposite  direction. 

These  laws  once  established,  it  became  possible  to  calculate  the  mo- 
tion of  any  body  or  system  of  bodies  when  once  the  forces  which  act 
on  them  were  known,  and,  rice  versa,  to  define  what  forces  were  re- 
quisite to  produce  any  given  motion.  The  question  which  presented 
itself  to  the  mind  of  NEWTON  and  his  contemporaries  was  this :  Under 
what  law  of  force  will  planets  mote  round  t/ie  gun  in  accordance  with 
KEPLER'S  laws  f 

Supposing  a  body  to  move  around  in  a  circle,  and  putting  R  the 
radius  of  the  circle,  T  the  period  of  revolution,  HUYGIIENB  had  shown 
that  the  centrifugal  force  of  the  body,  or,  which  is  the  same  thing, 
the  attractive  force  toward  the  centre  which  would  keep  it  in  the 

»3 

circle,  was  proportional  to  -=^.  But  by  KEPLER'S  third  law  T*  is  pro- 
portional to  #*.  Therefore  this  centripetal  force  is  proportional  to 
-j=;that  Is,  to-nf.  Thus  it  followed  immediately  from  KEPLER'S 

third  law  that  the  central  force  which  would  keep  the  planets  in  their 
orbits  was  in  verily  as  the  square  of  the  distance  from  the  sun,  sup- 
posing each  orbit  to  be  circular.  The  first  law  of  motion  once  com- 
pletely understood,  it  was  evident  that  the  planet  needed  no  force 
impelling  it  forward  to  keep  up  its  motion,  but  that,  once  started,  it 
would  keep  on  forever. 

The  next  step  was  to  solve  the  problem,  What  law  of  force  will 
make  a  planet  describe  an  ellipse  around  the  sun,  having  the  latter 
in  one  of  its  foci?  Or,  supposing  a  planet  to  move  round  the  sun, 
the  latter  attracting  it  with  a  force  inversely  as  the  square  of  the  dis- 
tance; what  will  be  the  form  of  the  orbit  of  the  planet  if  it  is  not  cir- 
cular? A  solution  of  either  of  these  problems  was  beyond  the  power 
of  mathematicians  before  the  time  of  NEWTON;  and  it  thus  remained 
uncertain  whether  the  planets  moving  under  the  influence  of  the 
sun's  gravitation  would  or  would  not  describe  ellipses.  Unable,  at 


UNIVERSAL  GRAVITATION.  117 

first,  to  reach  a  satisfactory  solution,  NEWTON  attacked  the  problem 
in  another  direction,  starting  from  the  gravitation,  not  of  the  sun, 
but  of  the  earth,  as  explained  in  the  following  section. 

GRAVITATION  IN  THE  HEAVENS. 

The  reader  is  probably  familiar  with  the  story  of  NEW- 
TON and  the  falling  apple.  Although  it  has  no  authorita- 
tive foundation,  it  is  strikingly  illustrative  of  the  method 
by  which  NEWTON  must  have  reached  a  solution  of  the 
problem.  The  course  of  reasoning  by  which  he  ascended 
from  gravitation  on  the  earth  to  the  celestial  motions  was  as 
follows :  We  see  that  there  is  a  force  acting  all  over  the  earth 
by  which  all  bodies  are  drawn  toward  its  centre.  This 
force  is  called  gravitation.  It  extends  without  sensible 
diminution  to  the  tops  not  only  of  the  highest  buildings, 
but  of  the  highest  mountains.  How  much  higher  does  it 
extend?  Why  should  it  not  extend  to  the  moon?  If  it 
does,  the  moon  would  tend  to  drop  toward  the  earth,  just 
as  a  stone  thrown  from  the  hand  drops.  As  the  moon 
moves  round  the  earth  in  her  monthly  course,  there  must 
be  some  force  drawing  her  toward  the  earth;  else,  by  the 
first  law  of  motion,  she  would  fly  entirely  away  in  a  straight 
line.  Why  should  not  the  force  which  makes  the  apple 
fall  be  the  same  force  which  keeps  her  in  her  orbit?  To 
answer  this  question,  it  was  not  only  necessary  to  calculate 
the  intensity  of  the  force  which  would  keep  the  moon  her- 
self in  her  orbit,  but  to  compare  it  with  the  intensity  of 
gravity  at  the  earth's  surface.  It  had  long  been  known 
that  the  distance  of  the  moon  was  about  sixty  radii  of  the 
earth,  from  measures  of  her  parallax  (see  page  57).  If 
this  force  diminished  as  the  inverse  square  of  the  distance, 
then  at  the  moon  it  would  be  only  -^-^  as  great  as  at  the 


118  ASTRONOMY. 

surface  of  the  earth.  On  the  earth  a  body  falls  sixteen  feet 
in  a  second.  If,  then,  the  theory  of  gravitation  were  cor- 
rect, the  moon  ought  to  fall  towards  the  earth  ygV^  of  this 
amount,  or  about  -fa  of  an  inch  in  a  second.  The  moon 
being  in  motion,  if  we  imagine  it  moving  in  a  straight  line 
at  the  beginning  of  any  second,  it  ought  to  be  drawn  away 
from  that  line  -fa  of  an  inch  at  the  end  of  the  second. 
When  the  calculation  was  made  it  was  found  to  agree  ex- 
actly with  this  result  of  theory.  Thus  it  was  shown  that 
the  force  which  holds  the  moon  in  her  orbit  is  the  same 
force  that  makes  the  stone  fall,  diminished  as  the  inverse 
square  of  the  distance  from  the  centre  of  the  earth. 

It  thus  appeared  that  central  forces,  both  toward  the  sun 
and  toward  the  earth,  varied  inversely  as  the  squares  of  the 
distances.  KEPLER'S  second  law  showed  that  the  line  drawn 
from  the  planet  to  the  sun  would  describe  equal  areas  in 
equal  times.  NEWTON  showed  that  this  could  not  be  true 
unless  the  force  which  held  the  planet  was  directed  toward 
the  sun.  We  have  already  stated  that  the  third  law  showed 
that  the  force  was  inversely  as  the  square  of  the  distance, 
and  thus  agreed  exactly  with  the  theory  of  gravitation.  It 
only  remained  to  consider  the  results  of  the  first  law,  that 
of  the  elliptic  motion.  After  long  and  laborious  efforts, 
NEWTON  was  enaoled  to  demonstrate  rigorously  that  this 
law  also  resulted  from  the  law  of  the  inverse  square,  and 
could  result  from  no  other.  Thus  all  mystery  disappeared 
from  the  celestial  motions;  and  planets  were  shown  to  be 
simply  heavy  bodies  moving  according  to  the  same  laws  that 
were  acting  here  around  us,  only  under  very  different  cir- 
cumstances. All  three  of  KEPLER'S  laws  were  embraced  in 
the  single  law  of  gravitation  toward  the  sun.  The  sun  at- 
tracts the  planets  as  the  earth  attracts  bodies  here  around  us. 


UNIVERSAL   GRAVITATION.  119 

Mutual  Action  of  the  Planets. — By  NEWTON'S  third  law  of  motion, 
each  planet  must  attract  the  sun  with  a  force  equal  to  that  which  the 
sun  exerts  upon  the  planet.  The  moon  also  must  attract  the  earth 
as  much  as  the  earth  attracts  the  moon.  Such  being  the  case,  it 
must  be  highly  probable  that  the  planets  attract  each  other.  If  so, 
KEPLER'S  laws  can  only  be  an  approximation  to  the  truth.  The  sun, 
being  immensely  more  massive  than  any  of  the  planets,  overpowers 
their  attraction  upon  each  other,  and  makes  the  law  of  elliptic  mo- 
tion very  nearly  true.  But  still  the  comparatively  small  attraction 
of  the  planets  must  cause  some  deviations.  Now,  deviations  from 
the  pure  elliptic  motion  were  known  to  exist  in  the  case  of  several  of 
the  planets,  notably  in  that  of  the  moon,  which,  if  gravitation  were 
universal,  must  move  under  the  influence  of  the  combined  attraction 
of  the  earth  and  of  the  sun.  NEWTON,  therefore,  attacked  the  com- 
plicated problem  of  the  determination  of  the  motion  of  the  moon 
under  the  combined  action  of  these  two  forces.  He  showed  in  a 
general  way  that  its  deviations  would  be  of  the  same  nature  as  those 
shown  by  observation.  But  the  complete  solution  of  the  problem, 
which  required  the  answer  to  be  expressed  in  numbers,  was  beyond 
his  power. 

Gravitation  Resides  in  each  Particle  of  Matter,— Still 
another  question  arose.  Were  these  mutually  attractive 
forces  resident  in  the  centres  of  the  several  bodies  attracted, 
or  in  each  particle  of  the  matter  composing  them?  NEW- 
TON* showed  that  the  latter  must  be  the  case,  because  the 
smallest  bodies,  as  well  as  the  largest,  tended  to  fall  toward 
the  earth,  thus  showing  an  equal  gravitation  in  every  sepa- 
rate part.  It  was  also  shown  by  NEWTON  that  if  a  planet 
were  on  the  surface  of  the  earth  or  outside  of  it,  it  would 
be  attracted  with  the  same  force  as  if  the  whole  mass 
of  the  earth  were  concentrated  in  its  centre.  Putting 
together  the  various  results  thus  arrived  at,  NEWTON" 
was  able  to  formulate  his  great  law  of  universal  gravita- 
tion in  these  comprehensive  words:  "Every  particle  of 
matter  in  the  universe  attracts  every  other  particle  with 
a  force  directly  as  the  masses  of  the  two  particles,  and 


120  AST&ONOMY. 

inversely  as  the  square  of  the  distance  which  separates 
them." 

To  show  the  nature  of  the  attractive  forces  among  these  various 
particles,  let  us  represent  by  m  and  iri  the  masses  of  two  attracting 
bodies.  We  may  conceive  the  body  m  to  be  composed  of  m  par- 
ticles, and  the  other  body  to  be  composed  of  m'  particles.  Let  us 
conceive  that  each  particle  of  one  body  attracts  each  particle  of  the 

other  with  a  force  — .     Then  every  particle  of  m  will  be  attracted  by 

each  of  the  m'  particles  of  the  other,  and  therefore  the  total  attractive 

m' 
force  on  each  of  the  m  particles  will  be  —5-.     Each  of  the  m  particles 

being  equally  subject  to  this  attraction,  the  total  attractive  force  be- 
tween the  two  bodies  will  be  .  When  a  given  force  acts  upon 

a  body,  it  will  produce  less  motion  the  larger  the  body  is,  the  Mftrf- 
erntiug  force  being  proportional  to  the  total  attracting  force  divided 
by  the  mass  of  the  body  moved.  Therefore  the  accelerating  force 
which  acts  on  the  body  in',  and  which  determines  the  amount  of 

motion,  will  be  -^;  and  conversely  the  accelerating  force  acting  on 
the  body  m  will  be  represented  by  the  fraction  — ^-. 


REMARKS  ON  THE  THEORY  OF  GRAVITATION. 

The  real  nature  of  the  great  discovery  of  NEWTON  is  so 
frequently  misunderstood  that  a  little  attention  may  be 
given  to  its  elucidation.  Gravitation  is  frequently  spoken 
of  as  if  it  were  a  theory  of  NEWTON'S,  and  very  generally 
received  by  astronomers,  but  still  liable  to  be  ultimately 
rejected  as  a  great  many  other  theories  have  been.  Not 
infrequently  people  of  greater  or  less  intelligence  are  found 
making  great  efforts  to  prove  it  erroneous.  NEWTON  did 
not  discover  any  new  force,  but  only  showed  that  the 
motions  of  the  heavens  could  be  accounted  for  by  a  force 
which  we  all  know  to  exist.  Gravitation  (Latin  g radius — 


UNIVERSAL   GRAVITATION.  121 

weight,  heaviness)  is  the  force  which  makes  all  bodies 
here  at  the  surface  of  the  earth  tend  to  fall  downward; 
and  if  any  one  wishes  to  subvert  the  theory  of  gravitation, 
he  must  begin  by  proving  that  this  force  does  not  exist. 
This  no  one  would  think  of  doing.  What  NEWTON  did 
was  to  show  that  this  force,  which,  before  his  time,  had 
been  recognized  only  as  acting  on  the  surface  of  the  earth, 
really  extended  to  the  heavens,  and  that  it  resided  not  only 
in  the  earth  itself,  but  in  the  heavenly  bodies  also,  and  in 
each  particle  of  matter,  however  situated.  To  put  the 
matter  in  a  terse  form,  what  NEWTON  discovered  was  not 
gravitation,  but  the  universality  of  gravitation. 

It  may  be  inquired,  is  the  induction  which  supposes 
gravitation  universal  so  complete  as  to  be  entirely  beyond 
doubt?  We  reply  that  within  the  solar  system  it  certainly 
is.  The  laws  of  motion  as  established  by  observation  and 
experiment  at  the  surface  of  the  earth  must  be  considered 
as  mathematically  certain.  It  is  an  observed  fact  that  the 
planets  in  their  motions  deviate  from  straight  lines  in  a 
certain  way.  By  the  first  law  of  motion,  such  deviation 
can  be  produced  only  by  a  force;  and  the  direction  and 
intensity  of  this  force  admit  of  being  calculated  once  that 
the  motion  is  determined.  When  thus  calculated,  it  is 
found  to  be  exactly  represented  by  one  great  force  con- 
stantly directed  toward  the  sun,  and  smaller  subsidiary 
forces  directed  toward  the  several  planets.  Therefore  no 
fact  in  nature  is  more  firmly  established  than  that  of  uni- 
versal gravitation,  as  laid  down  by  NEWTON,  at  least  within 
the  solar  system. 

We  shall  find,  in  describing  double  stars,  that  gravita- 
tion is  also  found  to  act  between  the  components  of  a  great 
number  of  such  stars.  It  is  certain,  therefore,  that  at 


ASTRONOMY. 


least  some  stars  gravitate  toward  each  other,  as  the  bodies 
of  the  solar  system  do;  but  the  distance  which  separates 
most  of  the  stars  from  each  other  and  from  our  sun  is  so 
immense  that  no  evidence  of  gravitation  between  in  dividual 
stars  and  the  sun  has  yet  been  given  by  observation.  Still, 
that  they  do  gravitate  according  to  NEWTON'S  law  can 
hardly  be  seriously  doubted  by  any  one  who  understands 
the  subject. 

The  student  may  now  l>e  supposed  to  see  the  absurdity 
of  supposing  that  the  tlioory  of  gravitation  can  ever  be 
subverted.  It  is  not,  however,  absurd  to  suppose  that  it 
may  yet  be  shown  to  be  the  result  of  some  more  general 
law.  Attempts  to  do  this  arc  made  from  time  to  time 
by  men  of  a  philosophic  spirit;  but  thus  far  no  theory  of 
the  subject  having  much  probability  in  its  favor  has  been 
propounded. 


CHAPTER  VII. 
THE  MOTIONS  AND  ATTRACTION  OF  THE  MOON. 

EACH  of  the  planets,  except  Mercury  and  Venus,  is  at- 
tended by  one  or  more  satellites,  or  moons  as  they  are 
sometimes  familiarly  called.  These  objects  revolve  around 
their  several  planets  in  nearly  circular  orbits,  accompany- 
ing them  in  their  revolutions  around  the  sun.  Their  dis- 
tances from  their  planets  are  very  small  compared  with  the 
distances  of  the  latter  from  each  other  and  from  the  sun. 
Their  magnitudes  also  are  very  small  compared  with  those 
of  the  planets  around  which  they  revolve.  Considering 
each  system  by  itself,  the  satellites  revolve  around  their 
central  planets,  or  "  primaries,"  in  nearly  circular  orbits, 
and  in  each  system  KEPLER'S  laws  govern  the  motion  of  the 
satellites  about  the  primary.  Each  system  is  carried  around 
the  sun  without  any  derangement  of  the  motion  of  its  sev- 
eral bodies  among  themselves. 

Our  earth  has  a  single  satellite  accompanying  it  in  this 
way,  the  moon.  It  revolves  around  the  earth  in  a  little 
less  than  a  month.  The  nature,  causes,  and  consequences 
of  this  motion  form  the  subject  of  the  present  chapter. 

THE  MOON'S  MOTIONS  AND  PHASES. 

That  the  moon  performs  a  monthly  circuit  in  the  heavens  is  a  fact 
with  which  we  are  all  familiar  from  childhood.  At  certain  times  we 
see  her  newly  emerged  from  the  sun's  rays  in  the  western  twilight, 
and  then  we  call  her  the  new  moon.  On  each  succeeding  evening 


124  ASTRONOMY. 

we  see  her  further  to  the  east,  so  that  in  two  weeks  she  is  opposite 
the  sun,  rising  in  the  east  as  he  sets  in  the  west.  Continuing  her 
course  two  weeks  more,  she  has  approached  the  sun  on  the  other 
side,  or  from  the  west,  and  is  once  more  lost  in  his  rays.  At  the  end 
of  twenty- nine  or  thirty  days,  we  see  her  again  emerging  as  new 
moon,  and  her  circuit  is  complete.  The  sun  has  been  apparently 
moving  toward  the  east  among  the  stars  during  the  whole  month,  so 
that  during  the  interval  from  one  new  moon  to  the  next  the  moon 
has  to  make  a  complete  circuit  relatively  to  the  stars,  and  to  move 
forward  some  30°  further  to  overtake  the  sun,  which  has  also  been 
moving  toward  the  east  at  the  rate  of  1°  daily.  The  revolution  of 
the  moon  among  the  stars  is  performed  in  about  27£  days,*  so  that  if 
we  observe  when  the  moon  is  very  near  some  star,  we  shall  find  her 
in  the  same  position  relative  to  the  star  at  the  end  of  this  interval. 

The  motion  of  the  moon  in  this  circuit  differs  from  the  apparent 
motions  of  the  planets  in  l>eing  always  forward.  We  have  seen  that 
the  planets,  though,  on  the  whole,  moving  toward  the  east,  are 
effected  with  an  apparent  retrograde  motion  at  certain  intervals,  ow- 
ing to  the  motion  of  the  earth  around  the  sun.  But  the  earth  is  Die 
real  centre  of  the  moon's  motion,  and  carries  the  moon  along  with  it 
in  its  annual  revolution  around  the  sun.  To  form  a  correct  idea  of 
the  real  motion  of  these  three  bodies,  we  must  imagine,  the  earth  per- 
forming its  circuit  around  the  sun  in  one  year,  and  carrying  with  it 
the  moon,  which  makes  a  revolution  around  it  in  27  days,  at  a  dis- 
tance only  about  ffa  that  of  the  sun. 

Phases  of  the  Moon. — The  moon,  being  a  non-luminous 
body,  shines  only  by  reflecting  the  light  falling  on  her  from 
some  other  body.  The  principal  source  of  light  is  the  sun. 
Since  the  moon  is  spherical  in  shape,  the  sun  can  illumi- 
nate one  half  her  surface.  The  appearance  of  the  moon 
varies  according  to  the  amount  of  her  illuminated  hemi- 
sphere which  is  turned  toward  the  earth,  as  can  be  seen  by 
studying  Fig.  39.  Here  the  central  globe  is  the  earth; 
the  circle  around  it  represents  the  orbit  of  the  moon.  The 
rays  of  the  sun  fall  on  both  earth  and  moon  from  the 
right,  the  distance  of  the  sun  being,  on  the  scale  of  the 

*  More  exactly,  27.32166-1. 


MOTIONS  AND  ATTRACTION  OF  THE  MOON.    125 

figure,  some  30  feet.  Eight  positions  of  the  moon  are 
shown  around  the  orbit  at  A,  E,  C,  etc.,  and  the  right- 
hand  hemisphere  of  the  moon  is  illuminated  in  each  posi- 
tion. Outside  these  eight  positions  are  eight  others  show- 
ing how  the  moon  looks  as  seen  from  the  earth  in  each 
position. 

At  A  ifc  is  "new  moon,"  the  moon  being  nearly  between 


FIG.  39. 

the  earth  and  the  sun.  Its  dark  hemisphere  is  then  turn- 
ed toward  the  earth,  so  that  it  is  entirely  invisible.  The 
sun  and  moon  then  rise  and  set  together. 

At  E  the  observer  on  the  earth  sees  about  a  fourth  of 
the  illuminated  hemisphere,  which  looks  like  a  crescent,  as 
shown  in  the  outside  figure.  In  this  position  a  great  deal 
of  light  is  reflected  from  the  earth  to  the  moon,  rendering 


126  ASTRONOMY. 

the  dark  part  of  the  latter  visible  by  a  gray  light.  This 
appearance  is  sometimes  called  the  "old  moon  in  the  new 
moon's  arms."  At  O  the  moon  is  said  to  be  in  her  "first 
quarter,"  and  one  half  her  illuminated  hemisphere  is  visi- 
ble. The  moon  is  on  the  meridian  at  6  P.M.  At  G  three 
fourths  of  the  illuminated  hemisphere  is  visible,  and  at  B 
the  whole  of  it.  The  latter  position,  when  the  moon  is 
opposite  the  sun,  is  called  "full  moon."  The  moon  rises 
at  sunset.  After  this,  at  //,  D,  F,  the  same  appearances 
are  repeated  in  the  reversed  order,  the  position  D  being 
called  the  "  last  quarter." 

THE  TIDES. 

It  is  not  possible  in  an  elementary  treatise  to  give  a  complete  ac- 
count of  the  theory  of  the  tides  of  the  ocean  due  to  the  effect  of  the 
sun  and  moon.  A  general  account  may  be  presented  which  will  be 
sufficient  to  show  the  nature  of  the  effects  produced  and  of  their 
causes.  (See  Fig.  39*.) 

Let  us  consider  the  earth  to  be  composed  of  a  solid  centre  sur- 
rounded by  an  ocean  of  uniform  (and  not  very  great)  depth.  The 
moon  exercises  an  attraction  upon  every  particle  of  the  earth's  mass, 
solid  and  fluid  alike.  The  attraction  of  the  whole  moon  (M)  upon 

a  particle  m  is  — ~,  where  p  is  the  distance  from  the  centre  of  the 

moon  to  m.     If  m  is  one  of  the  solid  particles  of  the  earth,  it  cannot 
move  towards  M  in  obedience  to  the  attraction  unless  all  the  other 
solid  particles  move,  since  the  earth  proper  is  rigid. 
If  m  is  a  fluid  particle,  it  is  free  to  move  in  obedience  to  the  forces 

impressed  upon  it.     The  attraction  of  M  is  proportional  to  — ;  that  is, 

P9 

the  particles  nearest  M  are  most  attracted,  and,  on  the  whole,  the 
water  on  the  part  of  the  earth  nearest  the  moon  will  be  raised  to- 
ward M. 

The  moon  also  attracts  the  solid  parts  of  the  earth  more  than  she 
attracts  the  water  most  distant  from  her,  and  this  produces  exactly 
the  same  effect  as  if  there  was  another  moon  M'  exactly  opposite  to 
M.  The  elevation  of  the  water  under  M'  will  not  be  quite  as  great 
as  that  under  M,  on  account  of  the  increased  distance  from  M. 


MOTIONS  AND  ATTRACTION  OF  THE  MOON.     127 

Thus  the  moon's  action  tends  to  elevate  the  whole  mass  of  water  on 
the  line  joining  her  centre  with  the  centre  of  the  earth,  and  this  is  so 
not  only  on  the  part  of  this  line  nearest  the  moon,  but  also  on  that 
farthest  from  her. 

This  elevation  of  the  waters  of  the  ocean  above  their  mean  level  is 
called  the  tide.  The  tidal  effect  of  the  moon  produces  a  distortion  of 
the  spherical  shell  of  water  which  we  have  supposed  to  surround  the 
earth, and  elongates  this  shell  into  the  shape  of  an  ellipsoid,  the  longer 
axis  of  which  is  always  directed  to  the  moon.  Now  as  the  moon 
moves  around  the  earth  once  in  24h  54m,  this  ellipsoidal  shape  must 
also  move  with  her.  The  crest  of  the  wave  directly  under  M  would 
come  back  to  the  same  meridian  every  241'  54m.  The  outer  crest  (under 
M' )  would  come  12h  27m  after  the  first,  so  there  would  be  two  high 
tides  at  any  one  meridian  every  (lunar)  day.  The  first  (and  largest) 
high  tide  would  be  at  the  time  of  the  moon's  visible  transit  over  the 
meridian.  The  second  high  tide  would  be  12h  27m  later,  when  the 
moon  was  on  the  lower  meridian  of  the  place. 

The  high  tides  occur  when  there  is  more  water  than  the  mean 
depth,  anil  between  these  high  tides  we  should  have  low  tides,  two 
in  each  lunar  day.  Similarly  there  would  be  two  high  tides  daily  at 
each  meridian,  due  to  the  attractive  force  of  the  sun.  These  would 
have  a  period  of  24  hours  and  could  not  always  agree  with  the  lunar 
high  tides.  When  Uie  solar  and  lunar  high  tides  coincided  (at  new 
and  full  moon)^then  we  should  have  the  highest  high  tides  and  the 
lowest  low  tides.  (These  are  the  Spring  tides,  so  called.)  When  the 
moon  and  the  sun  were  90°  apart  (moon  at  first  and  third  quarter), 
then  we  should  have  the  lowest  high  tides  and  the  highest  low  tides. 
(Neap  tides,  so  called.) 

The  tide-producing  force  of  the  moon  is  to  that  of  the  sun  as  800  is 
to  355.  The  great  mass  of  the  sun  compensates  in  some  degree  "for 
his  relatively  great  distance. 

At  spring  tides  sun  and  moon  work  together;  at  neap  tides  they 
oppose  each  other.  The  relative  heights  are  as  800  -f  355  :  800  —  355, 
or  as  13  to  5  approximately. 

The  explanation  above  relates  to  an  earth  covered  by  an  ocean  of 
uniform  depth.  To  fit  it  to  the  facts  as  they  are,  a  thousand  cir- 
cumstances must  be  taken  into  account,  Avhich  depend  upon  the 
modifying  effects  of  continents  and  islands,  of  deep  and  shallow 
seas,  of  currents  and  winds.  Practically,  the  high  tide  at  any  sta- 
tion is  predicted  by  adding  to  the  time  of  the  moon's  transit  over 
its  meridian  a  quantity  determined  from  observation  and  not  from 
theory. 


128  ASTRONOMY. 

Effects  of  the  Tides  upon  the  Earth's  Rotation. — As  the  tide-wave 
moves  it  meets  with  resistance  due  to  friction.  The  amount  of  this 
resistance  is  subtracted  daily  from  the  earth's  energy  of  rotation 
The  tides  act  on  the  earth,  in  a  way,  as  if  they  were  a  light  friction- 
brake  applied  to  an  enormously  heavy  wheel  turning  rapidly.  The 
wheel  has  been  set  to  turning,  and,  so  far  as  we  know,  it  will  never 
have  any  more  rotative  energy  given  to  it.  •  Every  subtraction  of 
energy,  however  small,  is  a  positive  and  irretrievable  loss. 

The  lunar  tides  are  gradually,  though  very  slowly,  lengthening  the 
day.  Since  accurate  astronomical  observations  began  there  has  been 
no  observational  proof  of  any  appreciable  change  in  the  length  of  the 
day,  but  the  change  has  been  going  on  nevertheless. 


Fio.  39«. 

In  the  figure  M  is  the  moon  on  the  meridian  Om  of  a 
place  m.  It  is  high  water  at  m  and  m'.  It  is  low  water 
at  m"  and  m'".  In  an  hour  the  moon  will  have  moved -to 
1'  and  the  crest  of  the  wave  to  1.  The  tide  will  be  high 
at  1  and  falling  at  m.  As  the  moon  moves  by  the  diurnal 
motion  to  2',  3',  M' ",  M' ,  the  crest  will  move  with  it. 
When  the  moon  is  at  M"'  it  is  low  water  at  m  and  m'. 
When  the  moon  is  at  M',  it  is  again  high  water  at  m;  and 
so  on.  If  we  suppose  M  to  be  the  sun,  a  similar  set  of 
solar  tides  will  be  produced  every  24  hours.  The  actual 
tide  is  produced  by  the  superposition  of  the  solar  and 
lunar  tides. 


CHAPTER  VIII. 
ECLIPSES  OF  THE  SUN  AND  MOON. 

ECLIPSES  are  phenomena  arising  from  the  shadow  of  one 
body  being  cast  upon  another,  or  from  a  dark  body  passing 
over  a  bright  one.  In  an  eclipse  of  the  sun,  the  shadow  of 
the  moon  sweeps  over  the  earth,  and  the  sun  is  wholly  or 
partially  obscured  to  observers  on  that  part  of  the  earth 
where  the  shadow  falls.  In  an  eclipse  of  the  moon,  the 
latter  enters  the  shadow  of  the  earth,  and  is  wholly  or 
partially  obscured  in  consequence  of  being  deprived  of 
some  or  all  of  its  borrowed  light.  The  satellites  of  other 
planets  are  from  time  to  time  eclipsed  in  the  same  way  by 
entering  the  shadows  of  their  primaries  ;  among  these  the 
satellites  of  Jupiter  are  objects  whose  eclipses  may  be 
observed  with  great  regularity. 

THE  EARTH'S  SHADOW  AND  PENUMBRA. 

In  Fig.  40  let  S  represent  the  sun,  and  E  the  earth.  Draw  straight 
lines,  DBVand  D'B'V,  each  tangent  to  the  sun  and  the  earth. 
The  two  bodies  being  supposed  spherical,  these  lines  will  be  the 
intersections  of  a  cone  with  the  plane  of  the  paper,  and  may  be 
taken  to  represent  that  cone.  It  is  evident  that  the  cone  B  VB'  will 
be  the  outline  of  the  shadow  of  the  earth,  and  that  within  this  cone 
no  direct  sunlight  can  penetrate.  It  is  therefore  called  the  earth's 
shadow-cone. 

Let  us  also  draw  the  lines  D'BP  and  DB'P'  to  represent  the 
other  cone  tangent  to  the  sun  and  earth.  It  is  then  evident  that 
within  the  region  VBP  and  VB'P'  the  light  of  the  sun.  will  be 
partially  but  not  entirely  cut  off. 


130 


ASTRONOMY. 


Dimensions  of  Shadow. — Let  us  investigate  the  distance  E  V  from 
Hie  centre  of  the  earth  to  the  vertex  of  the  shadow.  The  triangles 
V EB  and  VSD  are  similar,  having  a  right  angle  at  B  and  at  D. 
Hence 

VE:EB  =  VS:SD  =  ES:(8D-EB). 

So  if  we  put 

I  =  VE,  the  length  of  the  shadow  measured  from  the  centre  of 
the  earth, 

r  =  E S,  the  radius- vector  of  the  earth, 
R  =  SD,  the  radius  of  the  sun, 
p  =  EB,  the  radius  of  the  earth, 


we  have 


1=  VE  = 


E8X  EB 
8D-EB~  R-  p 


rp 


FIG.  40.— FORM  OK  SHADOW. 

That  is,  I  is  expressed  in  terms  of  known  quantities,  and  thus  is 
known. 

The  radius  of  the  shadow  diminishes  uniformly  with  the  distance 
as  we  go  outward  from  the  earth.     At  any  distance  z  from  the 

earth's  centre  it  will  be  equal  to  II  —  -\p,  for  this  formula  gives 

the  radius  p  when  2  =  0,  and  the  diameter  zero  when  z  =  I  as  it 
should.* 


*  It  will  be  noted  that  this  expression  is  not,  rigorously  speaking,  the  semi- 
diameter  of  the  shadow,  but  the  shortest  distance  from  a  point  on  its  central 
line  to  its  conical  surface.  This  distance  is  measured  in  a  direction  EB  perpen- 
dicular to  DB,  whereas  the  diameter  would  be  perpendicular  to  the  axis  SE^ 
and  its  half  length  would  be  a  little  greater  than  EB. 


ECLIPSES  OF  THE  SUN  AND  JfcfrMf  >  %     131 


ECLIPSES  OF  THE  MOON. 

The  mean  distance  of  the  moon  from  the  earth  is  about 
60  radii  of  the  latter,  and  the  length  E  V  of  the  earth's 
shadow  is  217  radii  of  the  earth.  Hence  when  the  moon 
passes  through  the  shadow  she  does  so  at  a  point  less  than 
three  tenths  of  the  way  from  E  to  V.  The  radius  of  the 
shadow  here  will  be  '3L^fSL  of  the  radius  E  B  of  the  earth, 
a  quantity  which  we  readily  find  to  be  about  4600  kilo- 
metres. The  radius  of  the  moon  being  1736  kilometres,  it 
will  be  entirely  enveloped  by  the  shadow  when  it  passes 
through  it  within  2864  kilometres  of  the  axis  E  V  of  the 
shadow.  If  its  least  distance  from  the  axis  exceed  this 
amount,  a  portion  of  the  lunar  globe  will  be  outside  the 
limits  B  V  of  the  shadow-cone,  and  will  therefore  receive  a 
portion  of  the  direct  light  of  the  sun.  If  the  least  distance 
of  the  centre  of  the  moon  from  the  axis  of  the  shadow  is 
greater  than  the  sum  of  the  radii  of  the  moon  and  the 
shadow — that  is,  greater  than  6336  kilometres — the  moon 
will  not  enter  the  shadow  at  all,  and  there  will  be  no  eclipse 
proper,  though  the  brilliancy  of  the  moon  is  diminished 
wherever  she  is  within  the  penumbral  region. 

When  an  eclipse  of  the  moon  occurs,  the  phases  are  laid  down 
in  the  almanac.  (See  Fig.  40.)  Supposing  the  moon  to  be  moving 
around  the  earth  from  below  upward,  its  advancing  edge  first 
meets  the  boundary  BP  of  the  penumbra.  The  time  of  this 
occurrence  is  given  in  the  almanac  as  that  of  "  moon  entering 
penumbra."  A  small  portion  of  the  sunlight  is  then  cut  off  from  the 
advancing  edge  of  the  moon,  and  this  amount  constantly  increases 
until  the  edge  reaches  the  boundary  B'  V  of  the  shadow.  It  is 
curious,  however,  that  the  eye  can  scarcely  detect  any  diminution  in 
the  brilliancy  of  the  moon  until  she  has  almost  touched  the  boundary 
of  the  shadow.  The  observer  must  not,  therefore,  expect  to  detect  the 
coming  eclipse  until  very  nearly  the  time  given  in  the  almanac  as  that 


ASTRONOMY. 


of  "moon  entering  shadow."  As  this  happens,  the  advancing 
portion  of  the  lunar  disk  will  be  entirely  lost  to  view,  as  if  it  were 
cut  off  by  n  rather  ill-defined  line.  It  takes  the  moon  about  an  hour 
to  move  pver  a  distance  equal  to  her  own  diameter,  so  that  if  the 
eclipse  is  nearly  central  the  whole  moon  will  be  immersed  in  the 
shadow  about  an  hour  after  she  first  strikes  it.  This  is  the  time  of 
beginning  of  total  eclipse.  So  long  as  only  a  moderate  portion  of 
the  moon's  disk  is  in  the  shadow,  that  portion  will  be  entirely 
invisible,  but  if  the  eclipse  becomes  total  the  whole  disk  of  the  moon 
will  nearly  always  be  plainly  visible,  shining  with  a  red  coppery 
light.  This  is  owing  to  the  refraction  of  the  sun's  rays  by  the  lower 
strata  of  the  earth's  atmosphere.  We  shall  see  hereafter  that  if  a  ray 
of  light  D  B  passes  from  the  sun  to  the  earth,  so  as  just  to  graze  the 
latter,  it  is  bent  by  refraction  more  than  a  degree  out  of  its  course, 
so  that  at  the  distance  of  the  moon  the  whole  shadow  of  the  earth 
is  filled  with  this  refracted  light.  An  observer  on  the  moon  would, 
during  a  total  eclipse  of  the  latter,  see  the  earth  surrounded  by  u 
ring  of  light,  anil  this  ring  would  appear  red,  owing  to  the  absorp- 
tion of  the  blue  and  green  rays  by  the  earth's  atmosphere,  just  as  the 
sun  seems  red  when  setting. 

The  moon  may  remain  enveloped  in  the  shadow  of  the  earth 
during  a  period  ranging  from  a  few  minutes  to  nearly  two  hours, 
according  to  the  distance  at  \\hicli  she  passes  from  the  axis  of  the 
shadow  and  the  velocity  of  her  angular  motion.  When  she  leaves 
the  shadow,  the  phases  which  we  have  described  occur  in  reverse 
order. 

It  very  often  happens  that  the  moon  passes  through  the  penumbra 
of  the  earth  without  touching  the  shadow  at  all.  The  diminution  of 
light  in  such  cases  is  scarcely  perceptible  unless  the  moon  at  least 
grazes  the  edge  of  the  shadow. 


ECLIPSES  OF  THE  Sire. 

In  Fig.  40  we  may  suppose  B  E  B'  to  represent  the 
moon.  The  geometrical  theory  of  the  shadow  will  remain 
the  same,  though  the  actual  length  of  the  shadow  in 
miles  will  be  much  less.  The  mean  length  of  the  moon's 
shadow  cast  by  the  sun  is  377,000  kilometres.  This  is 
nearly  equal  to  the  distance  of  the  moon  from  the  earth 
when  she  is  in  conjunction  with  the  sun.  We  therefore 


ECLIPSES  OF  THE  SUN  AN. 


conclude  that  when  the  moon  passes  between  the  earth 
and  the  sun,  the  former  will  be  very  near  the  vertex  F  of 
the  shadow.  As  a  matter  of  fact,  an  observer  on  the 
earth's  surface  will  sometimes  pass  through  the  region 
C  V  Cf,  and  sometimes  on  the  other  side  of  F. 

Now,  in  Fig.  40,  still  supposing  BEB'  to  be  the  moon,  and 
8  DD'  to  be  the  sun,  let  us  draw  the  lines  DB'P  and  D'BP  tan- 
gent to  both  moon  and  sun,  but  crossing  each  other  between  these 
bodies  at  b.  It  is  evident  that  an  observer  outside  the  space 
PBB'P  will  see  the  whole  sun,  no  part  of  the  moon  being  project- 
ed upon  it;  while  within  this  space  the  sun  will  be  more  or  less 
obscured.  The  whole  obscured  space  may  be  divided  into  three 
regions,  in  each  of  which  the  character  of  the  phenomenon  is  dif- 
ferent. 

First,  we  have  the  region  BVB'  forming  the  shadow-cone  proper. 
Here  the  sunlight  is  entirely  cut  off  by  the  moon,  and  darkness  is 
therefore  complete,  except  so  far  as  light  may  enter  by  refraction 
or  reflection.  To  an  observer  at  V  the  moon  would  exactly  cover 
the  sun,  the  two  bodies  being  apparently  tangent  to  each  other  all 
around. 

Secondly,  we  have  the  conical  region  to  the  right  of  V  between 
the  lines  B  V  and  B'  F  continued.  In  this  region  the  moon  is  seen 
wholly  projected  upon  the  sun,  the  visible  portion  of  the  latter 
presenting  the  form  of  a  ring  of  light  around  the  moon.  This  ring 
of  light  will  be  wider  in  proportion  to  the  apparent  diameter  of  the 
sun,  the  farther  out  we  go,  because  the  moon  will  appear  smaller 
than  the  sun,  and  its  angular  diameter  will  diminish  in  a  more  rapid 
ratio  than  that  of  the  sun.  This  region  is  that  of  annular  eclipse, 
because  the  sun  will  present  the  appearance  of  an  annulus  or  ring  of 
light  around  the  moon. 

Thirdly,  we  have  the  region  PBV  and  P'B'  V,  which  we  notice 
is  continuous,  extending  around  the  interior  cone.  An  observer 
here  would  see  the  moon  partly  projected  upon  the  sun,  and  there- 
fore a  certain  part  of  the  sun's  light  would  be  cut  off.  Along  the 
inner  boundary  B  V  and  B  V  the  obscuration  of  the  sun  will  be 
complete,  but  the  amount  of  sunlight  will  gradually  increase  out  to 
the  outer  boundary  B  P  B  P ,  where  the  whole  sun  is  visible.  This 
region  of  partial  obscuration  is  called  the  penumbra. 

To  show  more  clearly  the  phenomena  of  solar  eclipses,  we  present 
another  figure  representing  the  penumbra  of  the  moon  thrown  upon 


134 


ASTRONOMY. 


the  earth.*  The  outer  of  the  two  circles  S  represents  the  limb  of  the 
sun.  The  exterior  tangents  which  mark  the  boundary  of  the  shadow 
cross  each  other  at  V  before  reaching  the  earth.  The  earth  (K)  being 
a  little  beyond  the  vertex  of  the  shadow,  there  can  be  no  total  eclipse. 
In  this  case  an  observer  in  the  penumbral  region,  CO  or  DO,  will 
see  the  moon  partly  projected  on  the  sun,  while  if  he  chance  to  be 
situated  at  0  he  will  see  an  annular  eclipse.  To  show  how  this 
is,  we  draw  dotted  lines  fiom  0  tangent  to  the  moon.  The  angle 
between  these  lines  represents  the  apparent  diameter  of  the  moon  as 
seen  from  the  earth.  Continuing  them  to  the  sun,  they  show  the 
apparent  diameter  of  the  moon  as  projected  upon  the  sun.  It  will 
be  seen  that,  in  the  case  supposed,  when  the  vertex  of  the  shadow 
is  between  the  earth  and  moon  the  latter  will  necessarily  appear 


Fio.  41.— FIGURE  OF  SHADOW  FOR  ANNULAR  ECLIPSE. 

smaller  than  the  sun,  and  the  observer  will  see  a  portion  of  the  solar 
disk  on  all  sides  of  the  moon,  as  shown  in  Fig.  42. 

If  the  moon  were  a  little  nearer  the  earth  than  it  is  represented 
in  Fig.  41,  its  shadow  would  reach  the  earth  in  the  neighborhood 
of  0.  We  should  then  have  a  total  eclipse  at  each  point  of  the  earth 
on  which  it  fell.  It  will  be  seen,  however,  that  a  total  or  annular 
eclipse  of  the  sun  is  visible  only  on  a  very  small  portion  of  the  earth's 
surface,  because  the  distance  of  the  moon  changes  so  little  that  the 
earth  can  never  be  far  from  the  vertex  V  of  the  shadow.  As  the 


*  It  will  be  noted  that  all  the  figures  of  eclipses  are  necessarily  drawn  very 
much  out  of  proportion.  Really  the  sun  is  400  times  the  distance  of  the  moon, 
which  again  is  60  times  the  radius  of  the  earth.  But  it  would  be  entirely  im- 
possible to  draw  a  figure  of  this  proportion;  we  are  therefore  obliged  to 
represent  the  earth  in  Fig.  41  as  larger  than  the  sun,  and  the  moon  as  nearly 
half  way  between  the  earth  and  sun. 


ECLIPSES  OF  THE  SUN  AND  MOON. 


135 


moon  moves  around  the  earth  from  west  to  east,  its  shadow,  whether 
the  eclipse  be  total  or  annular,  moves  in  the  same  direction.    The 

diameter  of  the  shadow  at  the    _ 

surface  of  the  earth  ranges  from 
zero  to  150  miles.  It  therefore 
sweeps  along  a  belt  of  the 
earth's  surface  of  that  breadth, 
in  the  same  direction  in  which 
the  earth  is  rotating.  The 
velocity  of  the  moon  relative  to 
the  earth  being  3400  kilometres 
per  hour,  the  shadow  would 
pass  along  with  this  velocity  if 
the  earth  did  not  rotate,  but 
owing  to  the  earth's  rotation 
the  velocity  relative  to  points 
on  its  surface  may  range  from 


Fia.  42.— DARK  BODY  OF  MOON  PROJECTED 

ON  SUN  DURING  AN  ANNULAR  ECLIPSE. 


2000  to  3400  kilometres  (1200 
to  2100  miles). 

The  reader  will  readily  understand  that  in  order  to  see  a  total 
eclipse  an  observer  must  station  himself  beforehand  at  some  point  of 
the  earth's  surface  over  which  the  shadow  is  to  pass.  These  points 
are  generally  calculated  some  years  in  advance,  in  the  astronomical 
ephemerides. 


It  will  be  seen  that  a  partial  eclipse  of  the  sun  may  be 
visible  from  a  much  larger  portion  of  the  earth's  surface 
than  a  total  or  annular  one.  The  space  CD  (Fig.  41)  over 
which  the  penumbra  extends  is  generally  of  about  one  half 
the  diameter  of  the  earth.  Roughly  speaking,  a  partial 
eclipse  of  the  sun  may  sweep  over  a  portion  of  the  earth's 
surface  ranging  from  zero  to  perhaps  one  fifth  or  one  sixth 
of  the  whole. 

There  are  really  more  eclipses  of  the  sun  than  of  the 
moon.  A  year  never  passes  without  at  least  two  of  the 
former,  and  sometimes  five  or  six,  while  there  are  rarely 
more  than  two  eclipses  of  the  moon,  and  in  many  years 
none  at  all.  But  at  any  one  place  more  eclipses  of  the 


136  ASTRONOMT. 

moon  will  be  seen  than  of  the  sun.  The  reason  of  this  is 
that  an  eclipse  of  the  moon  is  visible  over  the  entire  hemi- 
sphere of  the  earth  on  which  the  moon  is  shining,  and  as 
it  lasts  several  hours,  observers  who  are  not  in  this  hemi- 
sphere at  the  beginning  of  the  eclipse  may,  by  the  earth's 
rotation,  be  brought  into  it  before  it  ends.  Thus  the 
eclipse  will  be  seen  over  more  than  half  the  earth's  surface. 
But,  as  we  have  just  seen,  each  eclipse  of  the  sun  can  be 
seen  over  only  so  small  a  fraction  of  the  earth's  surface  as 
to  more  than  compensate  for  the  greater  absolute  fre- 
quency of  solar  eclipses. 


Fio.  43.— COMPARISON  OF  SHADOW  AND  PENUMBRA  OF  EARTH  AND  MOON.    A  is 

THE  POSITION  OF  THK  MOON  DURING  A  SOLAR,  B  DURING  A  LUNAR,  ECLIPSE. 

It  will  be  seen  that,  in  order  to  have  either  a  total  or 
annular  eclipse  visible  upon  the  earth,  the  line  joining 
the  centres  of  the  sun  and  moon,  being  continued,  must 
strike  the  earth.  To  an  observer  on  this  line  the  centres 
of  the  two  bodies  will  seem  to  coincide.  An  eclipse  in 
which  this  occurs  is  called  a  central  one,  whether  it  be 
total  or  annular.  Fig.  43  will  perhaps  aid  in  giving  a 
clear  idea  of  the  phenomena  of  eclipses  of  both  sun  and 
moon. 

THE  RECURRENCE  OF  ECLIPSES. 

If  the  orbit  of  the  moon  around  the  earth  were  in  or  near  the 
plane  of  the  ecliptic  there  would  be  an  eclipse  of  the  sun  at  every 
new  moon,  and  an  eclipse  of  the  moon  at  every  full  moon.  But, 


ECLIPSES  OF  THE  SUN  AND  MOON.  137 

owing  to  the  inclination  of  the  moon's  orbit  (five  degrees  to  the 
ecliptic),  the  shadow  and  penumbra  of  the  moon  commonly  pass  above 
or  below  the  earth  at  the  time  of  new  moon,  while  the  moon,  at  her 
full,  commonly  passes  above  or  below  the  shadow  of  the  earth.  It 
is  only  when  the  moon  is  near  its  node  at  the  moment  of  new  or  full 
moon  that  an  eclipse  can  occur. 

The  question  now  arises,  how  near  must  the  moon  be  to  its  node 
in  order  that  an  eclipse  may  occur  ?  It  is  found  that  if,  at  the 
moment  of  new  moon,  the  moon  is  more  than  18° -6  from  its  node 
no  eclipse  of  the  sun  is  possible,  while  if  it  is  less  than  13°. 7  an 
eclipse  is  certain.  Between  these  limits  an  eclipse  may  occur  or  fail 
according  to  the  respective  distances  of  the  sun  and  moon  from  the 
earth.  Half  way  between  these  limits,  or  say  16°  from  the  node,  it 


FIG.  44.— Illustrating  lunar  eclipse  at  different  distances  from  the  node.  The 
dark  circles  are  the  earth's  shadow,  the  centre  of  which  is  always  in  the  ecliptic 
A  B.  The  moon's  orbit  is  represented  by  CD.  At  G  the  eclipse  is  central  and 
total,  at  F  it  is  partial,  and  at  E  there  is  barely  an  eclipse. 


is  an  even  chance  that  an  eclipse  will  occur;  toward  the  lower  limit 
(13°«7)the  chances  increase  to  certainty;  toward  the  upper  one 
(18° -6)  they  diminish  to  zero.  The  corresponding  limits  for  an 
eclipse  of  the  moon  are  9°  and  12$° ;  that  is,  if  at  the  moment  of  full 
moon  the  distance  of  the  moon  from  her  node  is  greater  than  13^° 
no  eclipse  can  occur,  while  if  the  distance  is  less  than  9°  an  eclipse 
is  certain.  We  may  put  the  mean  limit  at  11°.  Since,  in  the  long- 
run,  new  and  full  moon  will  occur  equally  at  all  distances  from  the 
node,  there  will  be,  on  the  average,  sixteen  eclipses  of  the  sun  to 
eleven  of  the  moon,  or  nearly  fifty  per  cent  more. 

If,  at  the  moment  of  new  moon,  the  distance  of  the  moon  from 
the  node  is  less  than  10|°  there  will  be  a  central  eclipse  of  the  sun, 
and  if  greater  than  this  there  will  not  be  such  an  eclipse.  The 


138  ASTRO  NOMT. 

eclipse  limit  may  range  half  a  degree  or  more  on  each  side  of  this 
mean  value,  owing  to  the  varying  distance  of  the  moon  from  the 
earth.  Inside  of  10°  a  central  eclipse  may  be  regarded  as  certain, 
and  outside  of  11°  as  impossible. 

If  the  direction  of  the  moon's  nodes  from  the  centre  of  the  earth 
were  invariable,  eclipses  could  occur  only  at  the  two  opposite  mouths 
of  the  year  when  the  sun  had  nearly  the  same  longitude  as  one  node. 
For  instance,  if  the  longitudes  of  the  two  opposite  nodes  were  re- 
spectively 54°  and  234°,  then,  since  the  sun  must  be  within  12°  of 
the  node  to  allow  of  an  eclipse  of  the  moon,  its  longitude  would  have 
to  be  either  between  42°  and  66°,  or  between  222"  and  246°.  But 
the  sun  is  within  the  first  of  these  regions  only  in  the  month  of  May, 
and  within  the  second  only  during  the  month  of  November.  Hence 
lunar  eclipses  could  then  occur  only  during  the  months  of  May  and 
November,  and  the  same  would  hold  true  of  central  eclipses  of  the 
sun.  Small  partial  eclipses  of  the  latter  might  be  seen  occasionally 
a  day  or  two  from  the  beginnings  or  ends  of  the  above  months,  but 
they  would  be  very  small  and  quite  rare.  Now,  the  nodes  of  the 
moon's  orbit  were  actually  in  the  above  directions  in  the  year  1873. 
Hence  during  that  .year  eclipses  occurred  only  in  May  and  No- 
vember. We  may  caJl  these  months  the  seasons  of  eclipses  for 
1873. 

There  is  a  retrograde  motion  of  the  moon's  nodes  amounting  to 
19^°  in  a  year.  The  nodes  thus  move  back  to  meet  the  sun  in  its 
annual  revolution,  and  this  meeting  occurs  about  20  days  earlier 
every  year  than  it  did  the  year  before.  The  result  is  that  the  season 
of  eclipses  is  constantly  shifting,  so  that  each  season  ranges  through- 
out the  whole  year  in  18-6  years.  For  instance,  the  season  corre- 
sponding to  that  of  November,  1873,  had  moved  back  to  July  and 
August  in  1878,  and  will  occur  in  May,  1882,  while  that  of  May, 
1873,  will  be  shifting  back  to  November  in  1882. 

It  may  be  interesting  to  illustrate  this  by  giving  the  days  in  which 
the  sun  is  in  conjunction  with  the  nodes  of  the  moon's  orbit  during 
several  years. 

Ascending  Node.  Descending  Node. 

1879.  January  24.  1879.  July  17. 

1880.  January  6.  1880.  June  27. 

1880.  December  18.  1881.  June  8. 

1881.  November  30.  1882.  May  20. 

1882.  November  12.  1883.  May  1. 

1883.  October  25.  1884.  April  12. 

1884.  October  8.  1885.  March  25. 


ECLIPSES  OF  THE  SUN  AND  MOON.  139 

During  these  years,  eclipses  of  the  moon  can  occur  only  within  11 
or  12  days  of  these  dates,  and  eclipses  of  the  sun  only  within  15  or 
16  days. 

In  consequence  of  the  motion  of  the  moon's  node,  three  varying 
angles  come  into  play  in  considering  the  occurrence  of  an  eclipse: 
the  longitude  of  the  node,  that  of  the  sun,  and  that  of  the  moon. 
One  revolution  of  the  moon  relatively  to  the  node  is  accomplished, 
on  the  average,  in  27-21222  days.  If  we  calculate  the  time  required 
for  the  sun  to  return  to  the  node,  we  shall  find  it  to  be  346-6201 
days. 

Now,  let  us  suppose  the  sun  and  moon  to  start  out  together  from 
a  node.  At  the  end  of  346-6201  days  the  sun,  having  apparently 
performed  nearly  an  entire  revolution  around  the  celestial  sphere,  will 
again  be  at  the  same  node,  which  has  moved  back  to  meet  it.  But  the 
moon  will  not  be  there.  It  will,  during  the  interval,  have  passed 
the  node  12  times,  and  the  13th  passage  will  not  occur  for  a  week. 
The  same  thing  will  be  true  for  18  successive  returns  of  the  sun  to 
the  node;  we  shall  not  find  the  moon  there  at  the  same  time  with 
the  sun;  she  will  always  have  passed  a  little  sooner  or  a  little  later. 
But  at  the  19th  return  of  the  sun  and  the  242d  of  the  moon,  the  two 
bodies  will  be  in  conjunction  within  half  a  degree  of  the  node.  We 
find  from  the  preceding  periods  that 

242  returns  of  the  moon  to  the  node  require  6585.357  days. 
19      "          "       sun      "        "  "        6585.780     " 

The  two  bodies  will  therefore  pass  the  node  within  10  hours  of 
each  other.  This  conjunction  of  the  sun  and  moon  will  be  the  223d 
new  moon  after  that  from  which  we  started.  Now,  one  lunation 
(that  is,  the  interval  between  two  consecutive  new  moons)  is,  in  the 
mean,  29.530588  days;  223  lunations  therefore  require  6585.32  days. 
The  new  moon,  therefore,  occurs  a  little  before  the  bodies  reach  the 
node,  the  distance  from  the  latter  being  that  over  which  the  moon 
moves  in  Od.036,  or  the  sun  in  Od.459.  This  distance  is  28'  of  arc, 
somewhat  less  than  the  apparent  semidiameter  of  either  body.  This 
would  be  the  smallest  distance  from  either  node  at  which  any  new 
moon  would  occur  during  the  whole  period.  The  next  nearest  ap- 
proaches would  have  occurred  at  the  35th  and  47th  lunations  respec- 
tively. The  35th  new  moon  would  have  occurred  about  6°  before 
the  two  bodies  arrived  at  the  node  from  which  we  started,  and  the 
47th  about  1|°  past  the  opposite  node.  No  other  new  moon  would 
so  near  a  node  before  the  223d  one,  which,  as  we  have  just 
.  would  occur  0°  28'  west  of  the  node.  This  period  of  223  new 


140  ASTRONOMY. 

moons,  or  18  years  11  days,  was  called  the  Saros  by  the  ancient  as- 
tronomers, and  by  means  of  it  they  predicted  eclipses. 

The  possibility  of  a  total  eclipse  of  the  sun  arises  from  the  occa- 
sional very  slight  excess  of  the  apparent  angular  diameter  of  the 
moon  over  that  of  the  sun  This  excess  is  so  slight  that  such  an 
eclipse  can  never  last  more  than  a  few  minutes.  It  may  be  of  inter- 
est to  point  out  the  circumstances  which  favor  a  long  duration  of 
totality.  These  are : 

(1)  That  the  moon  should  be  as  near  as  possible  to  the  earth,  or, 
technically  speaking,  in  perigee,  because  its   angular  diameter  as 
seen  from  the  earth  will  then  be  greatest. 

(2)  That  the  sun  should  be  near  its   greatest  distance  from   the 
earth,  or  in  apogee,  because  then  its  angular  diameter  will  l>e  the 
least     It  is  now  in  this  position  about  the  end  of  June;  hence  the 
most  favorable  time  for  a  total  eclipse  of  very  long  duration  is  in  the 
summer  months.     Since  the  moon  must  be  in  perigee  and  also  be- 
tween the  earth  and  sun,  it  follows  that  the  longitude  of  the  perigee 
must  i»f  nearly  that  of  the  sun.     The  longitude  of  the  sun  at  the 
end  of  June  being  100°,  this  is  the  most  favorable  longitude  of  the 
moon's  perigee. 

(3)  The  moon  must  be  very  near  the  node  in  order  that  the  centre 
of  the  shadow  may  fall  near  the  equator.     The  reason  of  this  condi- 
tion is  that  the  duration  of  a  total  eclipse  may  be  considerably  in- 
creased by  the  rotation  of  the  earth  on  its  axis.     We  have  seen  that 
the  shadow  sweeps  over  the  earth  from  west  toward  east  with  a 
velocity  of  about  3400  kilometres  per  hour.     Since  the  earth  rotates 
in  the  same  direction,  the  velocity  relative  to  the  observer  on  the 
earth's  surface  will  be  diminished  by  a  quantity  depending  on  this 
velocity  of  rotation,  and  therefore  greater  the  greater  the  velocity. 
The  velocity  of  rotation  is  greatest  at  the  earth's  equator,  where  it 
amounts  to  1660  kilometres  per  hour,  or  nearly  half  the  velocity  of 
the  moon's  shadow.     Hence  the  duration  of  a  total  eclipse  may,  with- 
in the  tropics,  be  nearly  doubled  by  the  earth's  rotation.     When  all 
the  favorable  circumstances  combine  in  the  way  we  have  just  de- 
scribed, the  duration  of  a  total  eclipse  within  the  tropics  will  be- 
about  seven  minutes  and  a  half.     In  our  latitude  the  maximum  du- 
ration will  be  somewhat  less,  or  not  far  from  six  minutes,  but  it  is 
only  on  very  rare  occasions,  hardly  once  in  many  centuries,  that  all 
these  favorable  conditions  can  be  expected  to  concur. 

Occultation  of  Stars  by  the  Moon. — A  phenomenon  which,  geomet- 
rically considered,  is  analogous  to  an  eclipse  of  the  sun  is  the  occul- 
tatlon  of  a  star  by  the  moon.  Since  all  Hie  bodies  of  the  solar  system 
are  nearer  than  the  fixed  stars,  it  is  evident  that  they  must  from 


ECLIPSES  OF  THE  SUN  AND  MOON.  141 

lime  to  time  pass  between  us  and  the  stars.  The  planets  are,  how- 
ever, so  small  that  such  a  passage  is  of  very  rare  occurrence,  and 
when  it  does  happen  the  star  is  generally  so  faint  that  it  is  rendered 
invisible  by  the  superior  light  of  the  planet  before  the  latter  touches 
it.  But  the  moon  is  so  large  and  her  angular  motion  so  rapid  that 
she  passes  over  some  star  visible  to  the  naked  eye  every  few  days. 
Such  phenomena  are  termed  occultations  of  stars  by  the  moon.  It 
must  not,  however,  be  supposed  that  they  can  be  observed  by  the 
naked  eye.  In  general,  the  moon  is  so  bright  that  only  stars  of  the 
first  magnitude  can  be  seen  in  actual  contact  with  her  limb,  and  even 
then  the  contact  must  be  with  the  uuilluminated  limb. 


CHAPTER  IX. 
THE  EARTH. 

OUR  object  in  the  present  chapter  is  to  trace  the  effects 
of  terrestrial  gravitation  and  to  study  the  changes  to  which 
it  is  subject  in  various  places.  Since  every  part  of  the 
earth  attracts  every  other  part  as  well  as  every  object  upon 
its  surface,  it  follows  that  the  earth  and  all  the  objects 
that  we  consider  terrestrial  form  a  sort  of  system  by  them- 
selves, the  parts  of  which  are  firmly  bound  together  by 
their  mutual  attraction.  This  attraction  is  so  strong  that 
it  is  found  impossible  to  project  any  object  from  the  sur- 
face of  the  earth  into  the  celestial  spaces.  Every  particle 
of  matter  now  belonging  to  the  earth  must,  so  far  as  we 
can  see,  remain  upon  it  forever. 

MASS  AND  DENSITY  OF  THE  EARTH. 

The  mass  of  a  body  may  be  defined  as  the  quantity  of  matter  it  con- 
tains. It  is  measured  by  the  product  of  its  volume  (  V)  by  its  density 
(Z>)  .  M  =  V  .  D.  For  another  body  M'  =  V.  1)',  and  for  equal  vol- 
umes V  =  V  and  M  :  M'  =  D  :  D'.  The  density  of  pure  water  at 
about  39°  Fahr.  is  taken  as  the  unit-density.  The  unit-volume  may 
be  taken  as  a  cubic  foot.  The  unit-mass  will  then  be  that  of  a  cubic 
foot  of  pure  water  at  39°  Fahr. 

The  weight  of  a  body  i»  the  force  with  which  it  is  attracted  to  the  cen- 
tre of  the  earth.  A  body  of  mass  m  is  attracted  by  the  earth's  mass 


M  by         t  where  r  is  the  distance  M  m.    (See  page  120.)    The  weight 
w  of  m  is  then  —5—.    The  weight  w'  of  another  body  m'  is  w  =  —  rs—  • 


THE  EARTH.  143 

If  the  bodies  are  at  the  same  place  on  the  earth  r  =  /  and  w  :  w'  = 
m  :  m',  or  the  weights  of  bodies  at  the  same  place  on  the  earth  are 
proportional  to  their  masses.  It  is  easy  to  measure  the  weights  of 
bodies  by  balancing  them  in  scales  against  certain  pieces  of  metal. 
Hence  by  weighing  two  bodies  of  weights  w  and  w'  we  can  deter- 
mine the  ratio  of  their  masses  m  and  m'.  If  m  is  a  cubic  foot  of 
water,  m'  is  the  absolute  mass  of  the  other  substance. 

The  weight  w  is  not  the  same  in  all  parts  of  the  earth,  nor  at  dif- 
ferent heights  above  the  earth's  surface.  It  is  therefore  a  variable 
quantity,  depending  upon  the  position  of  the  body,  while  the  mass 
of  the  body  is  something  inherent  in  it,  which  remains  constant 
wherever  the  body  may  be  taken,  even  if  it  is  carried  through  the 
celestial  spaces,  where  its  weight  would  be  reduced  to  almost  noth- 
ing. 

The  unit  of  mass  which  we  may  adopt  is  arbitrary.  Generally  the 
most  convenient  unit  is  the  weight  of  a  body  at  some  fixed  place  on 
the  earth's  surface — the  city  of  Washington,  for  example.  Suppose 
we  take  such  a  portion  of  the  earth  as  will  weigh  one  kilogramme  in 
Washington;  we  may  then  consider  the  mass  of  that  particular  lot  of 
earth  or  rock  as  the  unit  of  mass,  no  matter  to  what  part  of  the  uni- 
verse we  take  it.  Suppose,  also,  that  we  could  bring  all  the  matter 
composing  the  earth  to  the  city  of  Washington,  one  unit  of  mass  at 
a  time,  for  the  purpose  of  weighing-  it,  returning  each  unit  of  mass  to 
its  place  in  the  earth  immediately  after  weighing,  so  that  there  should 
be  no  disturbance  of  the  earth  itself.  The  sum-total  of  the  weights 
thus  found  would  be  the  mass  of  the  earth,  and  would  be  a  perfectly 
definite  quantity,  admitting  of  being  expressed  in  kilogrammes  or 
pounds.  We  can  readily  calculate  the  mass  of  a  volume  of  water 
equal  to  that  of  the  earth  because  we  know  the  magnitude  of  the 
earth  in  litres,  and  the  mass  of  one  litre  of  water.  Dividing  this 
into  the  mass  of  the  earth,  supposing  ourselves  able  to  determine 
this  mass,  and  we  shall  have  the  specific  gravity,  or  what  is  more 
properly  called  the  density,  of  the  earth :  D  —  M  -*-  M' . 

What  we  have  supposed  for  the  earth  we  may  imagine  for  any 
heavenly  body  ;  namely,  that  it  is  brought  to  the  city  of  Washington 
in  small  pieces,  and  there  weighed  one  piece  at  a  time.  Thus  the 
total  mass  of  the  earth  or  any  heavenly  body  is  a  perfectly  defined 
and  determinate  quantity. 

It  may  be  remarked  in  this  connection  that  our  units  of  weight,  the 
pound,  the  kilogramme,  etc.,  are  practically  units  of  mass  rather  than 
of  weight.  If  we  should  weigh  out  a  pound  of  tea  in  the  latitude  of 
Washington,  and  then  take  it  to  the  equator,  it  would  really  be  less 
heavy  at  the  equator  than  in  Washington;  but  if  we  take  a  pound 


144  ASTRONOMY. 

weight  with  us,  that  also  would  be  lighter  at  the  equator,  so  that  the 
two  would  still  balance  each  other,  and  the  tea  would  be  still  con- 
sidered as  weighing  one  pound.  Since  things  are  actually  weighed 
in  this  way  by  weights  which  weigh  one  unit  at  some  definite  place, 
say  Washington,  and  which  are  carried  all  over  the  world  without 
being  changed,  it  follows  that  a  body  which  has  any  given  weight  in 
one  place  will,  as  measured  in  this  way,  have  the  same  apparent 
weight  in  any  other  place,  although  its  real  weight  will  vary.  But 
if  a  spring- balance  or  any  other  instrument  for  determining  absolute 
weights  were  adopted,  then  we  should  find  that  the  weight  of  the 
same  body  varied  as  we  took  it  from  one  part  of  the  earth  to  another. 
Since,  however,  we  do  not  use  this  sort  of  an  instrument  in  weigh- 
ing, but  pieces  of  metal  which  arc  carried  about  without  change,  it 
follows  that  what  we  call  units  of  weight  are  properly  units  of  ma>s. 
Density  of  the  Earth. — We  see  that  all  bodies  around  us  tend  to  fall 
toward  the  centre  of  the  earth.  According  to  the  law  of  gravitation, 
this  tendency  is  not  simply  a  single  force  directed  toward  ilic  centre 
of  the  earth,  but  is  the  resultant  of  an  infinity  of  separate  forces 
arising  from  the  attractions  of  all  the  separate  parts  which  compose 
the  earth.  The  question  may  arise,  how  do  we  know  that  each 
particle  of  the  earth  attracts  a  stone  which  falls,  and  that  the  whole 
attraction  does  not  reside  in  the  centre  ?  The  proofs  of  this  are 
numerous,  and  consist  rather  in  the  exactitude  with  which  the 
theory  represents  a  great  mass  of  disconnected  phenomena  than  in 
any  one  principle  admitting  of  demonstration.  Perhaps,  however, 
the  most  conclusive  proof  is  found  in  the  observed  fact  that  masses 
of  matter  at  the  surface  of  the  earth  do  really  attract  each  other  as 
required  by  the  law  of  NEWTON.  It  is  found,  for  example,  that 
isolated  mountains  attract  a  plumb-line  in  their  neighborhood. 

It  is  noteworthy  that  though  astronomy  affords  us  the 
means  of  determining  with  great  precision  the  relative 
masses  of  the  earth,  the  moon,  and  all  the  planets,  it  does 
not  enable  us  to  determine  the  absolute  mass  of  any  hea- 
venly body  in  units  of  the  weights  we  use  on  the  earth. 
The  sun  has  about  328,000  times  the  mass  of  the  earth,  and 
the  moon  only  -g^  of  this  mass,  but  to  know  the  absolute 
mass  of  either  of  them  we  must  know  how  many  kilo- 
grammes of  matter  the  earth  contains.  To  determine  this 
we  must  know  the  mean  density  of  the  earth,  and  this  is 


THE  EARTH.  145 

something  about  which  direct  observation  can  give  us  no  in- 
formation, because  we  cannot  penetrate  more  than  an  in- 
significant distance  into  the  earth's  interior. 

The  only  way  to  determine  the  density  of  the  earth  is  to  find  how 
much  matter  it  must  contain  in  order  to  attract  bodies  on  its  surface 
with  a  force  equal  to  their  observed  weight;  that  is,  with  such  intensity 
that  at  the  equator  a  body  shall  fall  nearly  five  metres  in  a  second.  To 
find  this  we  must  know  the  relation  between  the  mass  of  a  body  and 
its  attractive  force.  This  relation  can  only  be  found  by  measuring 
the  attraction  of  a  body  of  known  mass. 

We  may  measure  the  attraction  of  a  body  of  known  mass  in  the 
following  ingenious  way.  In  Fig.  44a  let  11 1KL  be  a  cube  of  lead 
1  metre  on  each  edge.  Two  holes  are  bored  through  the  cube  at  D  F 
and  E  G.  A  pair  of  scales  A  B  G 
has  its  scale -pans  D  E  connected 
by  fine  wires  to  other  scale-pans, 
F  G,  below  the  block.  Suppose 
the  pans  empty  and  everything  at 
rest. 

I.  Put  a  weight  W  in  D,  and 
balance  the  scales  by  weights  in  G. 
At  D  the  total   attraction   is  the 
attraction  of    the    earth   plus  the 

attraction  of   the   block,  while  at  ~  FIG. 

G  we  have   the   attraction  of  the 

earth  (downwards)  minus  the  attraction  of  the  block  (upwards);  hence 

(1)  Weights  in  G  =  weight  in  D  -f-  2  attraction  of  block. 

II.  Put  the  weight  Win  F,  and  balance  the  scales  by  weights  in  E. 
At  F  the  total  attraction  is  earth  minus  block,  and  at  EH  is  earth 
plus  block ;  hence 

(2)  Weights  in  E  —  weight  in  F  —  2  attraction  of  block. 
Combining  these  equations  (1)  and  (2),  we  have 

Weights  in  G  —  weights  in  E  =  4  attraction  of  block, 
after  small  corrections  have  been  applied  for  the  difference  of  height 
of  D,  E,  F,  G,  etc. 

The  attraction  of  this  block,  which  has  a  known  mass  in  kilo- 
grammes, is  thus  known,  and  hence  the  general  relation  between  mass 
in  kilogrammes  and  attractions.  The  attraction  of  the  earth  is  known, 
since  it  is  such  as  to  attract  bodies  with  forces  equal  to  their  observed 
weights.  Therefore  the  mass  of  the  earth  expressed  in  kilogrammes 
is  known.  The  volume,  V,  of  the  earth  is  known  from  surveys;  its 


146  ABTBOffOMT. 

mass,  M,  is  now  known,  and  hence  its  density,  D.  The  relative  masses 
of  the  sun  and  earth  (and  other  planets)  are  known,  and  hence  their 
absolute  masses  in  kilogrammes  become  known  as  soon  as  we  have 
the  earth's  absolute  mass  in  kilogrammes,  determined  as  above. 

The  results  of  experiment  show  the  earth  to  be  about  5  times  as 
dense  as  water.  The  sun  is  only  \  as  dense  as  the  eurih.  Other  re- 
searches give  about  5-6  for  the  density  of  the  eailh;  this  is  more 
than  double  the  average  specific  gravity  of  the  rocks  which  compose 
the  surface  of  the  globe:  whence  it  follows  that  the  inner  portions  of 
the  earth  are  much  more  dense  than  the  outer  parts. 

LAWS  OF  TERRESTRIAL  GRAVITATION. 

The  earth  being  very  nearly  spherical,  certain  theorems  respecting 
the  attraction  of  spheres  may  be  applied  to  it.  The  demonstration 
of  these  theorems  requires  the  use  of  the  Integral  Calculus,  and  will 
be  omitted  here,  only  the  conditions  and  the  results  being  stated. 
Let  us  imagine  a  hollow  shell  of  matter,  of  which  the  internal  ami 
external  surfaces  are  both  spheres,  attracting  any  other  mass  of 
matter,  a  small  particle  we  may  suppose.  This  particle  will  be 
attracted  by  every  particle  cf  the  shell  with  a  force  inversely  as  the 
square  of  its  distance  from  it.  The  total  attraction  of  the  shell  will 
In-  i he  resultant  of  this  infinity  of  separate  attractive  forces. 

TIU<>I;I  M  I.  —  If  tl«'  )nirftcle  be  outxide  the  shell,  it  will  be  attracted 
as  iftlie  whole  inasnoftJie  thell  were  concentrated  in  its  centre, 

Tm.ouKM  II. — If  the  particle  he  iiixitle.  the  shell,  the  opposite  attrar- 
tt'onx  in  every  dirertimt  irffl  neutralize  ««-h  other,  no  matter  whereabout* 
in  tJie  interior  the  particle  may  be,  and  the  resultant  attraction  of  the 
shell  will  therefore  be  zero. 

To  apply  this  to  the  attraction  of  a  solid  sphere,  let  us  first  sup- 
pose a  body  either  outside  the  sphere  or  on  its  surface.  If  we  con- 
ceive the  sphere  as  made  up  of  a  great  number  of  spherical  shells,  the 

attracted  point  will  be  external  to  all  of 
them.  Since  each  shell  attracts  as  if 
its  whole  mass  were  in  the  centre,  it 
follows  that  the  whole  sphere  attracts 
a  body  upon  the  outside  of  its  surface 
as  if  its  entire  mass  were  concentrated 
at  its  centre. 

Let  us  now  suppose  the  attracted 
particle  inside  the  sphere,  as  at  P,  Fig. 
4o,  and  imagine  a  spherical  surface 
PQ  concentric  with  the  sphere  and 
passing  through  the  attracted  particle. 
45.  All  that  portion  of  the  sphere  lying 


THE  EARTH.  147 

outside  this  spherical  surface  will  be  a  spherical  shell  having  the 
particle  inside  of  it,  and  will  therefore  exert  no  attraction  whatever 
on  the  particle.  That  portion  inside  the  surface  will  constitute  a 
sphere  with  the  particle  on  its  surface,  and  will  therefore  attract  as 
if  all  this  portion  were  concentrated  in  the  centre.  To  find  what 
this  attraction  will  be,  let  us  first  suppose  the  whole  sphefe  of  equal 
density.  Let  us  put 

a,  the  radius  of  the  entire  sphere. 

r,  the  distance  PC  of  the  particle  from  the  centre. 

The  total  volume  of  matter  inside  the  sphere  P  Q  will  then  be,  by 

4 
geometry,—  xr3.    Dividing  by  the  square  of  the  distance  r,  we  see 

o 

that  the  attraction  will  be  represented  by 

4 


that  is,  inside  the  sphere  the  attraction  will  be  directly  as  the  dis- 
tance of  the  particle  from  the  centre.     If  the  particle  is  at  the  sur- 

4 
face  we  have  r  =  a,  and  the  attraction  is  —  it  a.     Outside  the   sur- 

o 
4 
face  the  whole  volume  of  the  sphere  —  it  a3  will  attract  the  particle, 

4      az 
and  the  attraction  will  be  —  it  —  5.    If  we  put  r  =  a  in  this  formula, 

we  shall  have  the  same  result  as  before  for  the  surface  attraction. 

Let  us  next  suppose  that  the  density  of  the  sphere  varies  from  its 
centre  to  its  surface,  so  as  to  be  equal  at  equal  distances  from  the 
centre.  We  may  then  conceive  of  it  as  formed  of  an  infinity  of  con- 
centric spherical  shells,  each  homogeneous  in  density,  but  not  of  the 
same  density  as  the  others.  Theorems  I.  and  II.  will  then  still 
apply,  but  their  result  will  not  be  the  same  as  in  the  case  of  a  homo- 
geneous sphere  for  a  particle  inside  the  sphere.  Referring  to  Fig. 
45,  let  us  put 

D,  the  mean  density  of  the  shell  outside  the  particle  P. 
D',  the  mean  density  of  the  portion  P  Q  inside  of  P. 

We  shall  then  have  : 

4 

Volume  of  the  shell,  —  it  (a?  —  r3).     Volume  of  the  inner  sphere, 
o 

4  it  r\    Mass  of  the  shell  =  vol.  X  D  =  -^  it  D  (a3  —  r3).    Mass  of  the 

O  w 


148  ASTRONOMY. 

inner  sphere  =  vol.  X D1  =  3-*  -ZXr1.      Mass  of  the  whole  sphere  = 

o 

sum  of  masses  of  shell  and  inner  sphere  =  g-  TT  I  D  a3  -{-  (2)'  —  D)  ?>3i. 
Attraction  of  the  whole  sphere  upon  a  point  at  its  surface  = 


Attraction  of  the  inner  sphere  (the  same  as  that  of  the  whole  shell) 
upon  a  point  at  P  =  — ^  =  -n  D'r. 

If,  as  in  the  case  of  the  earth,  the  density  continually  increases  to- 
ward the  centre,  the  value  of  D'  will  increase  also,  as  r  diminishes,  so 
that  gravity  will  diminish  less  rapidly  than  in  the  case  of  a  homo- 
geneous sphere,  and  may,  in  fact,  actually  increase  as  we  descend. 
To  show  this,  let  us  subtract  the  attraction  at  P  from  that  at  the  sur- 
face. The  difference  will  give  : 

Diminution  at  P  =  t  n  (j)a  -f  (D'  -  D)  ^  -  D'r) 

Now  let  us  suppose  r  a  very  little  less  than  a,  and  put  r  =  a  —  d ; 
d  will  then  be  the  depth  of  the  particle  below  the  surface. 

Cubing  this  value  of  r,  neglecting  the  higher  powers  of  d,  and 

ft 
dividing  by  a*,  we  find  —9  =  a—3d.      Substituting   in  the  above 

equation,  the  diminution  of  gravity  at  P  becomes  -$  n  (3D—  2'D)d. 

We  see  that  if  3  D  <  2  D'— that  is,  if  the  density  at  the  surface  is 
less  than  $  of  the  mean  density  of  the  whole  inner  mass — this  quan- 
tity will  beeomc  negative,  showing  that  the  force  of  gravity  will  be 
less  at  the  surface  than  at  a  small  depth  in  the  interior.  But  it  must 
ultimately  diminish,  because  it  is  necessarily  zero  at  the  centre.  It 
was  on  this  principle  that  Professor  AIRY  determined  the  density  of 
the  earth  by  comparing  the  vibrations  of  a  pendulum  at  the  bottom 
of  the  Harton  Colliery,  and  at  the  surface  of  the  earth  in  the  neigh- 
borhood. At  the  bottom  of  the  mine  the  pendulum  gained  about 
2§-5  per  day,  showing  the  force  of  gravity  to  be  greater  there  than  at 
the  surface. 

FIGURE   AND   MAGNITUDE  OF  THE  EARTH. 

If  the  earth  were  fluid  and  did  not  rotate  on  its  axis,  it 
would  assume  the  form  of  a  perfect  sphere.  The  opinion 


TEE  EARTH.  140 

is  entertained  that  the  earth  was  once  in  a  molten  state, 
and  that  this  is  the  origin  of  its  present  nearly  spherical 
form.  If  we  give  such  a  sphere  a  rotation  upon  its  axis, 
the  centrifugal  force  at  the  equator  acts  in  a  direction  op- 
posed to  gravity,  and  thus  tends  to  enlarge  the  circle  of 
the  equator.  It  is  found  by  mathematical  analysis  that  the 
form  of  such  a  revolving  fluid  sphere,  supposing  it  to  be 
perfectly  homogeneous,  will  be  an  oblate  ellipsoid  ;  that  is, 
all  the  meridians  will  be  equal  and  similar  ellipses,  having 
their  major  axes  in  the  equator  of  the  sphere  and  their 
minor  axes  coincident  with  the  axis  of  rotation.  Our  earth, 
however,  is  not  wholly  fluid,  and  the  solidity  of  its  conti- 
nents prevents  its  assuming  the  form  it  would  take  if  the 
ocean  covered  its  entire  surface.  By  the  figure  of  the 
earth  we  mean,  hereafter,  not  the  outline  of  the  solid  and 
liquid  portions  respectively,  but  the  figure  which  it  would 
assume  if  its  entire  surface  were  an  ocean.  Let  us 
imagine  canals  dug  down  to  the  ocean  level  in  every  direc- 
tion through  the  continents,  and  the  water  of  the  ocean  to 
be  admitted  into  them.  Then  the  curved  surface  touching 
the  water  in  all  these  canals,  and  coincident  with  the  sur- 
face of  the  ocean,  is  that  of  the  ideal  earth  considered  by 
astronomers.  By  the  figure  of  the  earth  is  meant  the  figure 
of  this  liquid  surface,  without  reference  to  the  inequalities 
of  the  solid  surface. 

We  cannot  say  that  this  ideal  earth  is  a  perfect  ellipsoid, 
because  we  know  that  the  interior  is  not  homogeneous,  but 
all  the  geodetic  measures  heretofore  made  are  so  nearly 
represented  by  the  hypothesis  of  an  ellipsoid  that  the  lat- 
ter is  a  very  close  approximation  to  the  true  figure.  The 
deviations  hitherto  noticed  are  of  so  irregular  a  character 
that  they  have  not  yet  been  reduced  to  any  certain  law. 


150  ASTRONOMY. 

The  largest  which  have  been  observed  seem  to  be  due  to 
the  attraction  of  mountains,  or  to  inequalities  in  the  den- 
sity of  the  rocks  beneath  the  surface. 

Method  of  Triangulation. — Since  it  is  practically  impossi- 
ble to  measure  around  or  through  the  earth,  the  magnitude 
as  well  as  the  form  of  our  planet  has  to  be  found  by  com- 
bining measurements  on  its  surface  with  astronomical  ob- 
servations. Even  a  measurement  on  the  earth's  surface 
made  in  the  usual  way  of  surveyors  would  be  impracticable, 
owing  to  the  intervention  of  mountains,  rivers,  forests,  and 
other  natural  obstacles.  The  method  of  triangulution  is 
therefore  universally  adopted  for  measurements  extending 
over  large  areas. 


FIG.  46.— A  PART  OF  THE  FRKNCH  TRIANOULATION  NEAR  PARIS. 

Triangulation  is  executed  in  the  following  way  :  Two  points,  a 
and  b,  a  few  miles  apart,  are  selected  as  the;  extremities  of  a  base- 
line. They  must  he  so  chosen  that  their  di  tunee  apart  can  be  accu- 
rately measured  by  rods  ;  the  intervening  ground  should  therefore 
be  as  level  and  free  from  obstruction  as  possible.  One  or  more  ele- 
vated points,  E  F,  etc.,  must  be  visible  from  one  or  both  ends  of  the 
base-line.  By  means  of  a  theodolite  and  by  observation  of  the  pole- 
star,  the  directions  of  these  points  relative  to  the  meridian  are  accu- 
rately observed  from  each  end  of  the  base,  as  is  also  the  direction  a  b 
of  the  base-line  itself.  Suppose  F  to  be  a  point  visible  from  each 
end  of  the  base,  then  in  the  triangle  a  b  F  we  have  the  length  a  b  de- 


THE  EARTH.  151 

termined  by  actual  measurement,  and  the  angles  at  a  and  b  deter- 
mined by  observations.  With  these  data  the  lengths  of  the  sides 
a F and  b  Fare  determined  by  a  simple  computation. 

The  observer  then  transports  his  instruments  to  F,  and  determines 
in  succession  the  direction  of  the  elevated  points  or  hills  D  E  O  HJ, 
etc.  He  next  goes  in  succession  to  each  of  these  hills,  and  determines 
the  direction  of  all  the  others  which  are  visible  from  it.  Thus  a  net- 
work of  triangles  is  formed,  of  which  all  the  angles  are  observed 
with  the  theodolite,  while  the  sides  are  successively  calculated  from 
the  first  base.  For  instance,  we  have  just  shown  how  the  side  aFis 
calculated;  this  forms  a  base  for  the  triangle  E  Fa,  the  two  remain- 
ing sides  of  which  are  computed.  The  side  E  F  forms  the  base  of 
the  triangle  Gr  EF,  the  sides  of  which  are  calculated,  etc.  In  this 
operation  more  angles  are  observed  than  are  theoretically  necessary 
to  calculate  the  triangles.  This  surplus  of  data  serves  to  insure  the 
detection  of  any  errors  in  the  measures,  and  to  test  their  accuracy  by 
the  agreement  of  their  results.  Accumulating  errors  are  further 
guarded  against  by  measuring  additional  sides  from  time  to  time  as 
opportunity  offers. 

Chains  of  triangles  have  thus  been  measured  in  Russia  and  Sweden 
from  the  Danube  to  the  Arctic  Ocean,  in  England  and  France  from 
the  Hebrides  to  Algiers,  in  this  country  down  nearly  our  entire  At- 
lantic coast  and  along  the  great  lakes,  and  through  shorter  distances 
in  many  other  countries.  An  east  and  west  line  is  now  being  run 
by  the  Coast  Survey  from  the  Atlantic  to  the  Pacific  Ocean.  Indeed 
it  may  be  expected  that  a  network  of  triangles  will  be  gradually  ex- 
tended over  the  surface  of  every  civilized  country,  in  order  to  con- 
struct perfect  maps  of  it. 

Suppose  that  we  take  two  stations,  a  and.;,  Fig.  46,  situated  north 
and  south  of  each  other,  determine  the  latitude  of  each,  and  calculate 
the  distance  between  them  by  means  of  triangles,  as  in  the  figure. 
It  is  evident  that  by  dividing  the  distance  in  kilometres  by  the  dif- 
ference of  latitude  in  degrees  we  shall  have  the  length  of  one  degree 
of  latitude.  Then  if  the  earth  were  a  sphere,  we  should  at  once  have 
its  circumference  by  multiplying  the  length  of  one  degree  by  360. 
It  is  thus  found  that  the  length  of  i  degree  is  a  little  more  than  111 
kilometres,  or  between  69  and  70  English  statute  miles.  Its  circum- 
ference is  therefore  about  40,000  kilometres,  and  its  diameter  between 
12,000  and  13,000.*  (25,000  and  8000  miles.) 

*  When  the  metric  system  was  originally  designed  by  the  French,  it  was  in- 
tended that  the  kilometre  should  be  „&,„,  of  the  distance  from  the  pole  of  the 
earth  to  the  equator.  This  would  make  a  degree  of  the  meridian  equal,  on  the 
averare,  to  111£  kilometres.  But  the  me:--  rctually  adopted  is  nearly  Tfo  of 
an  inch  too  short. 


152  ASTRONOMY. 

Owing  to  the  ellipticity  of  the  earth,  the  length  of  one  degree 
varies  with  the  latitude  and  the  direction  in  which  it  is  im-asim •<!. 
The  next  step  in  the  order  of  accuracy  is  to  find  the  magnitude  and 
the  form  of  the  earth  from  measures  of  long  arcs  of  latitude  (and 
sometimes  of  longitude)  made  in  different  regions,  especially  near 
the  equator  and  in  high  latitudes.  But  we  shall  still  find  that  dif- 
ferent combinations  of  measures  give  slightly  different  results,  both 
for  the  magnitude  and  the  ellipticity,  owing  to  the  irregularities  in 
the  direction  of  attraction  which  we  have  already  described.  The 
problem  is  therefore  to  find  what  ellipsoid  will  satisfy  the  measures 
with  the  least  sum-total  of  error.  New  and  more  accurate  solutions 
will  be  reached  from  time  to  time  as  geodetic  measures  are  extended 
over  a  wider  area.  The  following  are  among  the  most  recent  results: 


Fio.  47. 

the  earth's  polar  semidiameter,  6355-270  kilometres;  earth's  equatorial 
semidiameter,  6377 -377  kilometres  ;  earth's  compression,  ffa.-g  of  the 
equatorial  diameter  ;  earth's  eccentricity  of  meridian,  0-08319.  An- 
other result  is  that  of  Captain  CLARKE  of  England,  who  found: 
polar  semidiameter,  6356-456*  kilometres;  equatorial  semidiameter, 
6378-191  kilometres. 

Geographic  and  Geocentric  Latitudes. — An  obvious  result  of  the 
ellipticity  of  the  earth  is  that  the  plumb-line  does  not  point  toward 
the  earth's  centre.  Let  Fig.  47  represent  a  meridional  section  of  the 
earth,  NS  being  the  axis  of  rotation,  E  Q  the  plane  of  the  equator, 
and  0  the  position  of  the  observer.  The  line  HE,  tangent  to  the 

*  Captain  CLARKE'S  results  are  given  in  feet,  the  polar  radius  being  20,854,895 
feet,  the  equatorial  20,926,202.  These  numbers  are  in  the  proportion  292  :  293. 


THE  EARTH. 


earth  at  0,  will  then  represent  the  horizon  of  the  observer,  while  the 
line  ZN't  perpendicular  to  HE,  and  therefore  normal  to  the  earth 
at  0,  will  be  the  vertical  as  determined  by  the  plumb-line.  The  angle 
0  N'Q,  or  Z  0  Q',  which  the  observer's  zenith  makes  with  the  equa- 
tor will  then  be  his  astronomical  or  geographical  latitude.  This  is 
the  latitude  which  in  practice  we  always  have  to  use,  because  we 
are  obliged  to  determine  latitude  by  astronomical  observation,  and 
not  by  measurement  from  the  equator.  We  cannot  determine  the 
direction  of  the  true  centre  G  of  the  earth  by  direct  observation  of 
any  kind,  but  only  the  direction  of  the  plumb-line,  or  of  the  perpen- 
dicular to  a  fluid  surface.  Z  0  Q'  is  the  astronomical  latitude.  If, 
however,  we  conceive  the  line  CO  z  drawn  from  the  centre  of  the 
earth  through  0,  z  will  be  the  observer's  geocentric  zenith,  while  the 
angle  0  C  Q  will  be  his  geocentric  latitude.  It  will  be  observed  that  it 
is  the  geocentric  and  not  the  geographic  latitude  which  gives  the  true 
position  of  the  observer  relative  to  the  earth's  centre.  The  difference 
between  the  two  latitudes  is  the  angle  0  0  N'  or  Z  Oz  ;  this  is  called 
the  angle  of  1he  vertical.  It  is  zero  at  the  poles  and  at  the  equator,  be- 
cause here  the  normals  pass  through  the  centre  of  the  ellipse,  and  it 
attains  its  maximum  of  11'  30"  at  latitude  45°.  It  will  be  seen  that  the 
geocentric  latitude  is  always  less  than  the  geographic.  In  north 
latitudes  the  geocentric  zenith  is  south  of  the  apparent  zenith,  and  in 
southern  latitudes  north  of  it;  being  nearer  the  equator  in  each  case. 


MOTION  OF  THE  EARTH'S  Axis,  OR  PRECESSION  OF  THE 
EQUINOXES. 

Sidereal  and  Equinoctial  Year. — In  describing  the  appar- 
ent motion  of  the  sun,  two  ways  of  finding  the  time  of  its 
apparent  revolution  around  the  sphere  were  described ;  in 
other  words,  of  fixing  the  length  of  a  year.  One  of  these 
methods  consists  in  finding  the  interval  between  successive 
passages  of  the  sun  through  the  equinoxes,  or,  which  is  the 
same  thing,  across  the  plane  of  the  equator,  and  the  other 
by  finding  when  it  returns  to  the  same  position  among  the 
stars.  Two  thousand  years  ago  HIPPARCHUS  found,  by 
comparing  his  own  observations  with  those  made  two  cen- 
turies before  by  TIMOCHARIS,  that  these  two  methods  of 


154  ASTRONOMY. 

fixing  the  length  of  the  year  did  not  give  the  same  result. 
It  had  previously  been  considered  that  the  length  of  a  year 
was  about  365  J  days,  and  in  attempting  to  correct  this 
period  by  comparing  his  observed  times  of  the  sun's  pass- 
ing the  equinox  with  those  of  TIMOCHARIS,  HIPPARCHUS 
found  that  the  length  required  a  diminution  of  seven  or 
eight  minutes.  He  therefore  concluded  that  the  true  length 
of  the  equinoctial  year  was  365  days  5  hours  and  about  53 
minutes.  When,  however,  he  considered  the  return  of  the 
sun  not  to  the  equinox,  but  to  the  same  position  relative 
to  the  bright  star  Spica  Vinjinix,  he  found  that  it  took 
some  minutes  more  than  365J  days  to  complete  the  revolu- 
tion. Thus  there  are  two  years  to  be  distinguished,  the 
tropical  or  equinoctial  year  and  the  sidereal  year.  The 
first  is  measured  by  the  time  of  the  sun's  return  to  the 
equinox ;  the  second  by  its  return  to  the  same  position 
relative  to  the  stars.  Although  the  sidereal  year  is  the 
correct  astronomical  period  of  one  revolution  of  the  earth 
around  the  sun,  yet  the  equinoctial  year  is  the  one  to  be 
used  in  civil  life,  because  the  change  of  seasons  depends 
upon  that  year.  Modern  determinations  show  the  respec- 
tive lengths  of  the  two  years  to  be,  in  mean  solar  days: 

Sidereal  year,  365d  6h     9ra     98  =  365d.  25636. 

Equinoctial  year,       365d  5h  48m  46s  =  365d.24220. 

It  is  evident  from  this  difference  between  the  two  years 
that  the  position  of  the  equinox  among  the  stars  must  be 
changing,  and  that  it  must  move  toward  the  west,  because 
the  equinoctial  year  is  the  shorter.  This  motion  is  called 
the  precession  of  the  equinoxes,  and  amounts  to  about  50" 
per  year.  The  equinox  being  simply  the  point  in  which 
the  equator  and  the  ecliptic  intersect,  it  is  evident  that  it 


THE  EARTH.  155 

can  change  only  through  a  change  in  one  or  both  of  these 
circles.  HIPPARCHUS  found  that  the  change  was  in  the 
equator  and  not  in  the  ecliptic,  because  the  declinations 
of  the  stars  changed,  while  their  latitudes  did  not.  Since 
the  equator  is  defined  as  a  circle  everywhere  90°  distant 
from  the  pole,  and  since  it  is  moving  among  the  stars,  it 
follows  that  the  pole  must  also  be  moving  among  the  stars. 
But  the  pole  is  nothing  more  than  the  point  in  which  the 
earth's  axis  of  rotation  intersects  the  celestial  sphere:  the 
position  of  this  pole  in  the  celestial  sphere  depends  solely 
upon  the  direction  of  the  earth's  axis,  and  is  not  changed  by 
the  motion  of  the  earth  around  the  sun.  Hence  precession 
shows  that  the  direction  of  the  earth's  axis  is  continually 
changing.  Careful  observations  from  the  time  of  HIPPAR- 
CHUS until  now  show  that  the  change  in  question  consists 
in  a  slow  revolution  of  the  pole  of  the  earth  around  the  pole 
of  the  ecliptic  as  projected  on  the  celestial  sphere.  The 
rate  of  motion  is  such  that  the  revolution  will  be  completed 
in  between  25,000  and  26,000  years.  At  the  end  of  this 
period  the  equinox  and  solstices  will  have  made  a  complete 
revolution  in  the  heavens. 


The  nature  of  this  motion  will  be  seen  more  clearly  by  referring  to 
Fig.  32,  p.  93.  We  have  there  represented  the  earth  in  four  posi- 
tions during  its  annual  revolution.  We  have  represented  the  axis  as 
inclining  to  the  right  in  each  of  these  positions,  and  have  described 
it  as  remaining  parallel  to  itself  during  an  entire  revolution.  The 
phenomena  of  precession  show  that  this  is  not  absolutely  true,  but 
that,  in  reality,  the  direction  of  the  axis  is  slowly  changing.  This 
change  is  such  that,  after  the  lapse  of  some  6400  years,  the  north 
pole  of  the  earth,  as  represented  in  the  figure,  will  not  incline  to  the 
right,  but^  toward  the  observer,  the  amount  of  the  inclination  remain- 
ing nearly  the  same.  The  result  will  evidently  be  a  shifting  of  the 
seasons.  At  D  we  shall  have  the  winter  solstice,  because  the  north 
pole  will  be  inclined  toward  the  observer  and  therefore  from  the  sun, 


1/56  ASTRONOMY. 

while  at  A  we  shall  have  the  vernal  equinox  instead  of  the  winter 
solstice,  and  so  on. 

In  6400  years  more  the  north  pole  will  be  inclined  toward  the  left, 
and  the  seasons  will  be  reversed.  Another  interval  of  the  same 
length,  and  the  north  pole  will  be  inclined  from  the  observer,  the 
seasons  being  shifted  through  another  quadrant.  Finally,  at  the 
end  of  about  25,8uO  years,  the  axis  will  have  resumed  its  original 
direction. 

Precession  thus  arises  from  a  motion  of  the  earth  alone  and  not  of 
the  heavenly  bodies.  Although  the  direction  of  the  earth's  axis 
changes,  yet  tlie  position  of  tfiis  axis  rehitive  to  flu  crust  of  (he  earth 
remains  invariable.  Some  have  supposed  that  precession  would 
result  in  a  change  in  the  position  of  the  north  pole  on  the  surface  of 


Fio 


the  earth,  so  that  the  northern  regions  would  be  covered  by  the 
ocean  as  a  result  of  the  different  direction  in  which  the  ocean  would 
be  carried  by  the  centrifugal  force  of  the  earth's  rotation.  This,  how- 
ever, is  a  mistake.  It  has  been  shown  that  the  position  of  the  poles, 
and  therefore  of  the  equator,  on  the  surface  of  the  earth,  cannot 
change  except  from  some  variation  in  the  arrangement  of  the  earth's 
interior.  Scientific  investigation  has  yet  shown  nothing  to  indicate 
any  probability  of  such  a  change. 

The  motion  of  precession  is  not  uniform,  but  is  subject  to  several 
small  inequalities  which  are  called  nutation. 


THE  CAUSE  OF  PRECESSION. 

The  cause  of  precession,  etc.,  is  illustrated  in  the  figure,  which 
shows  a  spherical  earth  surrounded  by  a  ring  of  matter  at  the  equa- 
tor. If  the  earth  were  really  spherical  there  would  be  no  precessioa 
It  is,  however,  ellipsoidal  \vith.  a  protuberance  at  the  equator.  The 


THE  EAUTH.  157 

effect  of  this  protuberance  is  to  be  examined.  Consider  the  action 
between  the  sun  and  earth  alone.  If  the  ring  of  matter  were  absent, 
the  earth  would  revolve  about  the  sun  as  is  shown  in  Fig.  32,  p.  93 
(Seasons).  \4 

We  remember  that  the  sun's  N.  P.  D.  if  90°  at  the  equinoxes,  and 
66i°  and  113£°  at  the  solstices.  At  the  equinoxes  the  sun  is  in  the 
direction  Cm;  that  is,  NCm  is  90°.  At  the  winter  solstice  the  sun  is 
in  the  direction  Cc  ;  NCc  =  113i°.  It  is  clear  that  in  the  latter  case 
the  effect  of  the  sun  on  the  ring  of  matter  will  be  to  pull  it  down 
from  the  direction  Cm  towards  the  direction  Cc.  An  opposite  effect 
will  be  produced  by  the  sun  when  its  polar  distance  is  66^°. 

The  moon  also  revolves  round  the  earth  in  an  orbit  inclined  to  the 
equator,  and  in  every  position  of  the  moon  it  has  a  different  action 
on  the  ring  of  matter.  The  earth  is  all  the  time  rotating  on  its  axis, 
and  these  varying  attractions  of  sun  and  moon  are  equalized  and 
distributed  since  different  parts  of  the  earth  are  successively  presented 
to  the  attracting  body.  The  result  of  all  the  complex  motions  we 
have  described  is  a  conical  motion  of  the  earth's  axis  N  C  about  the 
line  CE. 

The  earth's  shape  is  not  that  given  in  the  figure,  but  it  is  an  ellip- 
soid of  revolution.  The  ring  of  matter  is  not  cou'fined  to  the  equator/ 
but  extends  away  from  it  in  both  directions.  The  effects  of  the 
forces  acting  on  the  earth  as  it  is  are  however,  similar  to  the  effects 
we  have  described. 


CHAPTER  X. 
CELESTIAL  MEASUREMENTS  OF  MASS  AND  DISTANCE. 

THE  CELESTIAL  SCALE  OF  MEASUREMENT. 

THE  units  of  length  and  mass  employed  by  astronomers 
are  necessarily  different  from  those  used  in  daily  life.  The 
distances  and  magnitudes  of  the  heavenly  bodies  are  never 
reckoned  in  miles  or  other  terrestrial  measures  for  astro- 
nomical purposes;  when  so  expressed  it  is  only  for  the  pur- 
pose of  making  the  subject  clearer  to  the  general  reader. 
The  units  of  weight  or  mass  are  also,  of  necessity,  astro- 
nomical and  not  terrestrial.  The  mass  of  a  body  may  be 
expressed  in  terms  of  that  of  the  sun  or  of  the  earth,  but 
never  in  kilogrammes  or  tons,  unless  in  popular  language. 
There  are  two  reasons  for  this  course.  One  is  that  in  most 
cases  celestial  distances  have  first  to  be  determined  in 
terms  of  some  celestial  unit — the  earth's  distance  from  the 
sun,  for  instance — and  it  is  more  convenient  to  retain  this 
unit  than  to  adopt  a  new  one.  The  other  is  that  the 
values  of  celestial  distances  in  terms  of  ordinary  terrestrial 
units  are  for  the  most  part  uncertain,  while  the  corre- 
sponding values  in  astronomical  units  are  known  with 
great  accuracy. 

An  extreme  instance  of  this  is  afforded  by  the  dimensions 
of  the  solar  system.  By  a  series  of  astronomical  observa- 
tions, investigated  by  means  of  KEPLER'S  laws  and  the 
theory  of  gravitation,  it  is  possible  to  determine  the  forms 


MEASUREMENTS  OF  MASS  AND  DISTANCE.      159 

of  the  planetary  orbits,  their  positions,  and  their  dimen- 
sions in  terms  of  the  earth's  mean  distance  from  the  sun 
as  the  unit  of  measure,  with  great  precision.  KEPLER'S 
third  law  enables  us  to  determine  the  mean  distance  of  a 
planet  from  the  sun  when  we  know  its  period  of  revolu- 
tion. All  the  major  planets,  as  far  out  as  Saturn,  have  been 
observed  through  so  many  revolutions  that  their  periodic 
times  can  be  determined  with  great  exactness — in  fact 
within  a  fraction  of  a  millionth  part  of  their  whole  amount. 
The  more  recently  discovered  planets,  Uranus  and  Nep- 
tune, will,  in  the  course  of  time,  have  their  periods  deter- 
mined with  equal  precision.  Then,  if  we  square  the  peri- 
ods expressed  in  years  and  decimals  of  a  year,  and  extract 
the  cube  root  of  this  square,  we  have  the  mean  distance 
of  the  planet  with  the  same  order  of  precision.  This 
distance  is  to  be  corrected  slightly  in  consequence  of  the 
attractions  of  the  planets  on  each  other,  but  these  correc- 
tions also  are  known  with  great  exactness.  Again,  the 
eccentricities  of  ihe  orbits  are  exactly  determined  by  care- 
ful observations  of  the  positions  of  the  planets  during  suc- 
cessive revolutions.  Thus  we  could  make  a  map  of  the 
planetary  orbits  so  exact  that  the  error  would  entirely 
elude  the  most  careful  scrutiny,  though  the  map  itself 
might  be  many  yards  in  extent. 

On  the  scale  of  this  same  map  we  could  lay  down  the 
magnitudes  of  the  planets  with  as  much  precision  as  our 
instruments  can  measure  their  angular  semidiameters. 
Thus  we  know  that  the  mean  diameter  of  the  sun,  as  seen 
from  the  earth,  is  32'-,  hence  we  deduce  from  formulae 
already  given  on  pages  5  and  57  that  the  diameter  of  the 
sun  is  .0093083  of  the  distance  of  the  sun  from  the  earth. 
We  can.  therefore,  on  our  supposed  map  of  the  solar  system, 


160  ASTRONOMY. 

lay  down  the  sun  in  its  true  size,  according  to  the  scale  of 
the  map,  from  data  given  directly  by  observation.  In  the 
same  way  we  can  do  this  for  each  of  the  planets,  the  earth 
and  moon  excepted.  There  is  no  immediate  and  direct 
way  of  finding  how  large  the  earth  or  moon  would  look 
from  a  planet;  whence  the  exception. 

But  without  further  special  research  into  this  subject, 
we  shall  know  nothing  about  the  scale  of  our  map.  That 
is,  we  have  no  means  of  knowing  how  many  miles  or  kilo- 
metres correspond  in  space  to  an  inch  or  a  foot  on  the  map. 
It  is  clear  that  in  order  to  fix  the  distances  or  the  magni- 
tudes of  the  planets  according  to  any  terrestrial  standard, 
we  must  know  this  scale.  Of  course  if  we  can  learn  either 
the  distance  or  magnitude  of  any  one  of  the  planets  laid 
down  on  the  map,  in  miles  or  in  semidiameters  of  the 
earth,  we  shall  be  able  at  once  to  find  the  scale.  But  this 
process  is  so  difficult  that  the  general  custom  of  astrono- 
mers is  not  to  attempt  to  use  a  scale  of  miles,  but  to  employ 
the  mean  distance  of  the  sun  from  the  earth  as  the  unit  in 
celestial  measurements.  Thus,  in  astronomical  language, 
we  say  that  the  distance  of  Mercury  from  the  sun  is  0.387, 
that  of  Venus  0.7^3,  that  of  Mars  1.523,  that  of  Saturn 
9.539,  and  so  on.  But  this  gives  us  no  information  respect- 
ing the  distances  and  magnitudes  in  terms  of  terrestrial 
measures.  The  unknown  quantities  of  our  map  are  the 
magnitude  of  the  earth  and  its  distance  from  the  sun  in 
terrestrial  units  of  length.  Could  we  only  take  up  a  point 
of  observation  on  the  sun  or  a  planet,  and  determine  ex- 
actly the  angular  magnitude  of  the  earth  as  seen  from  that 
point,  we  should  be  able  to  lay  down  the  earth  of  our  map 
in  its  correct  size.  Then,  since  we  already  know  the  size 
of  the  earth  in  terrestrial  units  from  geodetic  surveys  we, 


MEASUREMENTS  OF  MASS  AND  DISTANCE.    161 

should  be  able  to  find  the  scale  of  our  map,  and  thence 
the  dimensions  of  the  whole  system  in  terms  of  those 
units. 

It  will  be  seen  that  what  the  astronomer  really  wants  is 
not  so  much  the  dimensions  of  the  solar  system  in  miles  as 
to  express  the  size  of  the  earth  in  celestial  measures. 
This,  however,  amounts  to  the  same  tiling,  because  having 
one,  the  other  can  be  readily  deduced  from  the  known 
magnitude  of  the  earth  in  terrestrial  measures. 

The  magnitude  of  the  earth  is  not  Ihc  only  unknown 
quantity  on  our  map.  From  KEPLER'S  laws  we  can  deter- 
mine nothing  respecting  the  distance  of  the  moon  from  the 
earth,  because  unless  a  change  is  made  in  the  units  of  time 
and  space,  they  apply  only  to  bodies  moving  around  the 
sun.  We  must  therefore  determine  the  distance  of  the 
moon  as  well  as  that  of  the  sun  to  be  able  to  complete  our 
map  on  a  known  scale  of  measurement. 

MEASURES  OF  THE  SOLAR  AND  LUNAR  PARALLAX. 

The  problem  of  distances  in  the  solar  system  is  reduced 
by  the  preceding  considerations  to  measuring  the  distances 
of  the  sun  and  moon  in  terms  of  the  earth's  radius.  The 
most  direct  method  of  doing  this  is  by  determining  their 
respective  parallaxes,  which  we  have  shown  to  be  the  same 
as  the  earth's  angular  semidiameter  as  seen  from  them. 
In  the  case  of  the  sun,  the  required  parallax  can  be  deter- 
mined as  readily  by  measuring  the  parallaxes  of  any  of  the 
planets  as  by  measuring  that  of  the  sun,  because  any  one 
measured  distance  on  the  map  will  give  us  the  scale  of  our 
map,  Now,  the  planets  Venus  and  Mars  occasionally 
come  much  nearer  the  earth  than  the  sun  ever  does,  and 
tkeir  parallaxes  also  admit  of  more  exact  measurement. 


162  ASTRONOMY. 

The  parallax  of  the  sun  is  therefore  determined  not  by  ob- 
servations on  the  sun  itself,  but  on  these  two  planets. 

The  general  principles  of  the  method  of  determining  the 
parallax  of  a  planet  by  simultaneous  observations  at  distant 
stations  will  be  seen  by  referring  to  the  figure.  If  two 
observers,  situated  at  S'  and  S">  make  a  simultaneous 
observation  of  the  direction  of  the  body  P,  it  is  evident 
that  the  solution  of  a  plane  triangle  S'S"P  will  give  the  dis- 
tance of  P  from  each  station.  In  practice,  however,  it  would 


Fio.  49. 

be  impracticable  to  make  simultaneous  observations  at 
distant  stations;  and  as  the  planet  is  continually  in  motion, 
the  problem  is  a  much  more  complex  one  than  that  of 
simply  solving  a  triangle. 

This  is  the  method  of  determining  the  parallax  of  the 
moon.  Knowing  the  actual  figure  of  the  earth,  observa- 
tions of  the  moon  made  at  stations  widely  separated  in 
latitude,  as  Paris  and  the  Cape  of  Good  Hope,  can  be  com- 
bined so  as  to  give  the  parallax  of  the  moon  and  thus  its 
distance.  On  precisely  the  same  principles  the  parallaxes 
of  Venus  or  Mars  have  been  determined. 


MEASUREMENTS  OF  MASS  AND  DISTANCE.     163 

Solar  Parallax  from  Transits  of  Venus. — When  Venus  is  at  inferior 
conjunction  she  is  between  the  sun  and  the  earth.  If  her  orbit  lay 
in  the  ecliptic,  she  would  be  projected  on  the  sun's  disk  at  every  in- 
ferior conjunction.  The  inclination  of  her  orbit  is,  in  fact,  about  3|°, 
and  thus  transits  of  Venus  occur  only  when  she  is  near  the  node  of 
her  orbit  at  the  time  of  inferior  conjunction.  In  Fig.  49*  let  E,  V,  S 
be  the  earth,  Venus,  and  the  sun.  D  (7  is  Venus'  orbit.  An  observer 
B  will  see  Venus  impinge  on  the  sun's  disk  at  /,  be  just  internally 
tangent  at  II,  move  across  the  disk  to  III  and  off  at  1 V.  Similar 
phenomena  will  occur  for  A  at  1,  2,  3,  4.  When  A  sees  Venus  at  a, 
B  will  see  her  at  6.  a  b  is  the  parallax  of  Venus  with  respect  to  the 
change  of  position  A  B.  (See  page  56.)  a  b  :  A  B  ::  V a  :  VA;  but 
V A  :  Va  as  1:2£  nearly  (see  table  p.  198,  3d  column),  a  b  there- 
fore occupies  on  the  sun's  disk  a  space  2|  times  as  large  as  the  earth's 
diameter.  If  we  measure  the  angular  dimension  a  b  in  any  way, 
and  divide  the  resulting  angle  by  2|,  we  shall  have  the  angle  sub 
tended  at  the  sun  by  the  earth's  diameter;  or  if  we  divide  it  by  5, 
the  angle  subtended  by  the  earth's  radius.  This  is  nothing  but  the 
sun's  parallax.  (See  page  57.) 

The  angular  space  a  b  can  be  directly  measured  at  a  transit  of 
Venus,  or  it  may  be  calculated  when  we  know  the  length  of  the 
chords  //,  ///,  and  2,  3.  The  length  of  each  chord  is  known  by  ob- 


FIG.  49a. 

serving  the  interval  of  time  elapsed  from  phase  //  to  phase  III,  or 
better  by  observing  all  four  phases  and  making  the  proper  allowances. 

Other  Methods  of  Determining  Solar  Parallax. — A  very 
interesting  and  probably  the  most  accurate  method  of 
measuring  the  sun's  distance  depends  upon  a  knowledge  of 
the  velocity  of  light.  We  shall  hereafter  see  that  the  time 


164  ASTRONOMY. 

required  for  light  to  pass  from  the  sun  to  the  earth  is  known 
with  considerable  exactness,  being  very  nearly  498  seconds. 
This  time  can  be  determined  still  more  accurately.  If 
then  we  can  determine  experimentally  how  many  miles  or 
kilometres  light  moves  in  a  second,  we  shall  at  once  have 
the  distance  of  the  sun  by  multiplying  that  quantity  by 
498.  The  velocity  of  light  is  about  300,000  kilometres 
per  second.  This  distance  would  reach  about  eight  times 
around  the  earth.  It  is  seldom  possible  to  see  two  points 
on  the  earth's  surface  more  than  a  hundred  kilometres 
apart,  and  distinct  vision  at  distances  of  more  than  twenty 
kilometres  is  rare.  Hence  to  determine  experimentally  tin- 
time  required  for  light  to  pass  between  t\\<>  tern-stria!  sta- 
tions requires  the  measurement  of  an  interval  of  time 
which,  even  under  the  most  favorable  cases,  can  be  only  a 
fraction  of  a  thousandth  of  a  second.  Methods  of  doing 
it,  however,  have  been  devised,  and  the  velocity  of  light 
would  seem  to  be  about  299,900  kilometres  per  second. 
Multiplying  this  by  498,  we  obtain  149,350,000  kilometres 
(a  little  less  than  93,000,000  miles)  for  the  distance  of  the 
sun.  The  time  required  for  light  to  pass  from  the  sun  to 
the  earth  is  still  uncertain  by  nearly  a  second,  but  this 
value  of  the  sun's  distance  is  probably  the  best  yet  ob- 
tained. The  corresponding  value  of  the  sun's  parallax  is 
8'.  81. 

Yet  other  methods  of  determining  the  sun's  distance 
are  given  by  the  theory  of  gravitation.  It  is  found  by 
mathematical  investigation  that  the  motion  of  the  moon  is 
subject  to  several  inequalities,  having  the  sun's  horizontal 
parallax  as  a  factor.  If  the  position  of  the  moon  could  be 
determined  by  observation  with  the  same  exactness  that 
the  position  of  a  star  or  planet  can  (which  it  cannot  be), 


MEASUREMENTS  OF  MASS  AND  DISTANCE.     165 

this  would  probably  afford  the  most  accurate  method  of 
determining  the  solar  parallax. 

Brief  History  of  Determinations  of  the  Solar  Parallax. — The  determi- 
nation of  the  distance  of  the  sun  must  at  all  times  have  been  one  of 
the  most  interesting  scientific  problems  presented  to  the  human  mind. 
The  first  known  attempt  to  effect  a  solution  of  the  problem  was  made 
by  ARISTARCHUS,  who  flourished  in  the  third  century  before  CHRIST. 
It  was  founded  on  the  principle  that  the  time  of  the  moon's  first 
quarter  will  vary  with  the  ratio  between  the  distance  of  the  moon 
and  sun,  which  may  be  shown  as  follows.  In  Fig.  50  let  JE"  represent 
the  earth,  M  the  moon,  and  S  the  sun.  Since  the  sun  always 
illuminates  one  half  of  the  lunar  globe,  it  is  evident  that  when  one 


FIG.  50. 

half  of  the  moon's  disk  appears  illuminated  the  triangle  E  MS  must 
be  right  angled  at  M.  The  angle  ME  S  can  be  determined  by 
measurement,  being  equal  to  the  angular  distance  between  the  sun 
and  the  moon.  Having  two  of  the  angles,  the  third  can  be  deter- 
mined, because  the  sum  of  the  three  must  make  two  right  angles. 
Thence  we  shall  have  the  ratio  between  E  M,  the  distance  of  the  moon, 
and  E  S,  the  distance  of  the  sun,  by  a  trigonometrical  computation. 
Then  knowing  the  distance  of  the  moon,  which  can  be  determined 
with  comparative  ease  (see  page  162),  we  have  the  distance  of  the  sun 
by  multiplying  by  this  ratio.  ARISTARCHUS  concluded,  from  his 
supposed  measures,  that  the  angle  M  E  S  was  three  degrees  less  than 

JTI  -\r  -j 

a  right  angle.    We  should  then  have  -==-^-  =  —r  very  nearly,  since  3° 

Mi  o         1«7 

is  yj  of  57°  and  E  S  =  57°  (see  page  5).  It  would  follow  from  this 
that  the  sun  was  19  times  the  distance  of  the  moon,  We  now  know 


166  ASTRONOMY. 

that  this  result  is  entirely  wrong,  and  that  it  is  so  because  it  is  im- 
possible to  determine  the  time  when  the  moon  is  exactly  half  illumi- 
nated with  any  approach  to  the  accuracy  necessary  in  the  solution  of 
the  problem.  In  fact,  the  greatest  angular  distance  of  the  earth  and 
moon,  as  seen  from  the  sun — that  is,  the  angle  E SM — is  only  about 
one  quarter  the  angular  diameter  of  the  moon  as  seen  from  the 
earth. 

The  second  attempt  to  determine  the  distance  of  the  sun  is  men 
tioned  by  PTOLEMY,  though  HIPPAKCHUS  may  be  the  real  inventor 
of  it.  It  depends  on  the  dimensions  of  the  earth's  shadow-cone  dur- 
ing a  total  eclipse  of  the  moon.  It  is  only  necessary  to  state  the 
result,  which  was  that  the  sun  was  situated  at  the  distance  of  1210 
radii  of  the  earth.  This  result,  like  the  former,  was  due  only  to 
errors  of  observation.  So  far  as  all  the  methods  known  at  the  time 
could  show,  the  real  distance  of  the  sun  appeared  to  be  infinite; 
nevertheless  PTOLEMY'S  result  was  received  without  question  for 
fourteen  ceiilm  i» •-. 

Th?  first  renlly  successful  measure  of  the  parallax  of  a  planet  was 
made  upon  Mara  during  the  opposition  of  1672,  by  the  first  of  the 
two  methods  already  described.  An  expedition  was  sent  to  the 
colony  of  Cayenne  to  observe  the  declination  of  the  planet  from 
ni.irht  to  night,  while  corresponding  observations  were  made  at  the 
Paris  Observatory.  From  a  discussion  »>f  tlioe  observations,  CAB- 
BINI  obtained  a  solar  parallax  of  9". 5,  which  is  within  a  second  of 
the  truth.  The  next  steps  forward  were  made  by  the  transits  of 
Venus  in  1761  and  1769.  The  lending  civilized  nations  caused  obx  r- 
vations  on  these  transits  to  be  made  at  various  points  on  the  globe. 
The  method  used  was  very  simple,  consisting  in  the  determination 
of  the  times  at  which  Venus  entered  upon  the  sun's  disk  and  left  it 
again.  The  absolute  times  of  ingress  and  egress,  as  seen  from  differ- 
ent points  of  the  globe,  might  differ  by  20  minutes  or  more  on  ac- 
count of  parallax.  The  results,  however,  were  found  to  be  discord- 
ant. It  was  not  until  more  than  half  a  century  had  elapsed  that  the 
observations  were  systematically  calculated  by  ENCKE  of  Germany, 
who  concluded  that,  the  parallax  of  the  sun  was  8"  .578,  and  the  dis- 
tance 95  millions  of  miles. 

In  1854  it  began  to  be  suspected  that  ENCKE'S  value  of  the  parallax 
was  much  too  small.  HANSEN,  from  the  theory  of  the  moon,  found 
the  parallax  of  the  sun  to  be  8". 916.  This  result  seemed  to  be  con- 
firmed by  other  observations,  especially  those  of  Mars  during  1862. 
It  was  therefore  concluded  that  the  sun's  parallax  was  probably  be 
tween  8". 90  and  9". 00.  Subsequent  researches  have,  however,  been 
diminishing  this  value.  In  1867,  from  a  discussion  of  all  the  data 


MEASUREMENTS  OF  MASS  AND  DISTANCE.     167 

which  were  considered  of  value,  it  was  concluded  by  one  of  the 
writers  that  the  most  probable  parallax  was  8". 848.  The  measures 
of  the  velocity  of  light  reduce  this  value  to  8". 81,  and  it  is  now 
doubtful  whether  the  true  value  is  any  larger  than  this. 

All  we  can  say  at  present  is  that  the  solar  parallax  is  probably  be- 
tween 8". 79  and  8". 83,  or,  if  outside  these  limits,  that  it  can  be  very 
little  outside. 


RELATIVE  MASSES  OF  THE  SUN  AND  PLANETS, 

In  estimating  celestial  masses  as  well  as  distances,  it  is  necessary 
to  use  what  we  may  call  celestial  units;  that  is,  to  take  the  mass  of 
some  celestial  body  as  a  unit,  instead  of  any  multiple  of  the  pound  or 
kilogram.  The  reason  of  this  is  that  the  ratios  between  the  masses 
of  the  planetary  system,  or,  which  is  the  same  thing,  the  mass  of 
each  body  in  terms  of  that  of  some  one  body  as  the  unit,  can  be  de- 
termined independently  of  the  mass  of  any  one  of  them.  To  express 
a  mass  in  kilogrammes  or  other  terrestrial  units,  it  is  necessary  to  find 
the  mass  of  the  earth  in  such  units,  as  already  explained  This, 
however,  is  not  necessary  for  astronomical  purposes,  where  only  the 
relative  masses  of  the  several  planets  are  required.  In  estimating 
the  masses  of  the  individual  planets,  that  of  the  sun  is  generally 
taken  as  a  unit.  The  planetary  masses  will  then  all  be  very  small 
fractions. 

The  mass  of  the  sun  being  1.00,  the  mass  of  Mercury  is 

Venus  is 
Earth  is 
Mars  is 
Jupiter  is 
Saturn  is 
Uranus  is 
Neptune  is 

Masses  of  the  Earth  and  Sun.— The  mass  of  the  earth  is  connected 
by  a  very  curious  relation  with  the  parallax  of  the  sun.  Knowing 
the  latter,  we  can  determine  the  mass  of  the  sun  relative  to  the  earth, 
which  is  the  same  thing  as  determining  the  astronomical  mass  of  the 
earth,  that  of  the  sun  being  unity.  This  may  be  clearly  seen  by  re- 
flecting that  when  we  know  the  radius  of  the  earth's  orbit  we  can 
determine  how  far  the  earth  moves  aside  from  a  straight  line  in  one 
second  in  consequence  of  the  attraction  of  the  sun.  This  motion 
measures  the  attractive  force  of  the  sun  at  the  distance  of  the  earth. 


168 


ASTRONOMY. 


Comparing  it  with  the  attractive  force  of  the  earth,  and  making 
allowance  for  the  difference  of  distances  from  centres  of  the  two 
hodies,  we  determine  the  ratio  between  their  masses. 

The  following  table  shows,  for  different  values  of  the  solar  paral- 
lax, the  corresponding  ratio  of  the  musses,  and  distance  of  the  sun  in 
terrestrial  measures: 


DISTANCE  or  THE  SUN 

SOLAR 

M 

PARALLAX. 

r» 

m 

In  equatorial 
radii  of  the 
earth. 

In  millions  of 
mile* 

In  millions  of 
kil«>m»'tivs. 

8*.  77 

835684 

28519 

93.208 

150.001 

8".  78 

:m5tt 

MM 

93.102 

141.810 

8'.  79 

:{:{:!:ws 

28466 

92.996 

149.6(50 

8'.  80 

332262 

i:*9 

92.890 

Its.  490 

8'.  81 

831132 

idtl 

92.785 

149.:'.--M> 

8'.  82 

330007 

:IS6 

92.680 

149.151 

8*.  83 

328887 

::l«0 

92  .  575 

148.982 

We  havesnid  that  the  solar  parallax  is  probably  contained  between 
the  limits  8". 79  and  8". 83.  It  is  certainly  hardly  more  than  one  or 
two  hundredths  of  a  second  without  them.  So,  if  we  wish  to  ex- 
press the  constants  relating  to  the  sun  in  round  numbers,  we  may 
say  that — 

Its  mans  is  330,000  times  that  of  the  earth. 

Its  distance  in  miles  is  93  millions,  or  perhaps  a  little  less. 

Its  distance  in  kilometres  is  probably  between  149  and  150  mil- 
lions. 

The  masses  of  the  planets  with  satellites  are  determined  by  cal- 
culating what  mass  a  body  must  have  to  produce  the  observed  motion 
of  the  satellites.  The  planets  without  satellites  have  their  masses  de- 
termined by  calculating  what  mass  will  produce  such  perturbations 
of  the  motions  of  the  other  planets  as  are  actually  observed. 


CHAPTEK  XL 

THE  REFRACTION  AND  ABERRATION  OF  LIGHT  AND 
TWILIGHT. 

ATMOSPHERIC  REFRACTION. 

WHEN  we  speak  of  the  place  of  a  planet  or  star,  we  usu- 
ally mean  its  true  place;  i.e.,  its  direction  from  an  ob- 
server situated  at  the  centre  of  the  earth.  We  have  shown 
in  the  section  on  parallax  how  observations  which  are 
necessarily  taken  at  the  surface  of  the  earth  are  reduced 
to  what  they  would  have  been  if  the  observer  were  situated 
at  the  earth's  centre.  We  have  supposed  the  star  to  be 
projected  on  the  celestial  sphere  in  the  prolongation  of 
the  line  joining  the  observer  and  the  star.  The  ray  from 
the  star  was  considered  to  suffer  no  deflection  in  passing 
through  the  stellar  spaces  and  through  the  earth's  atmos- 
phere. But  from  the  principles  of  physics,  we  know  that 
such  a  luminous  ray  passing  from  an  empty  space  (as  the 
stellar  spaces  probably  are),  and  through  an  atmosphere, 
must  suffer  a  refraction,  as  every  ray  of  light  is  known  to 
do  in  passing  from  a  rare  into  a  denser  medium.  As  we 
see  the  star  in  the  direction  in  which  its  light  enters  the 
eye — that  is,  as  we  project  the  star  on  the  celestial  sphere 
by  prolonging  this  light-beam  backward  into  space — there 
must  be  an  apparent  displacement  of  the  star  from  refrac- 
tion. 

We  may  recall  a  few  definitions  from  physics.  The  ray  which 
leaves  the  star  and  impinges  on  the  outer  surface  of  the  earth's  at- 


170  ASTRONOMY. 

mospbcre  is  called  the  incident  ray  ;  after  its  deflection  by  the  atmos- 
phere it  is  called  the  refracted  ray.  The  difference  between  these 
directions  is  called  the  astronomical  refraction.  If  a  normal  is  drawn 
(perpendicular)  to  the  surface  of  the  refracting  medium  at  the  point 
where  the  incident  ray  meets  it,  the  acute  angle  between  the  incident 
ray  and  the  normal  is  called  the  angle  of  incidence,  and  the  ncutc  angle 

between  the  normal  and  the  refracted 
ray  is  called  the  angle  of  refraction. 
The  refraction  itself  is  the  difference 
of  these  angles.  The  normal  and 
both  incident  and  refracted  rays  are 
in  the  same  vertical  plane.  In  Fig. 
51.  SA  is  the  ray  incident  upon  the 
surface  HA  of  the  refracting  medium 
II  II  AN,  AC1  is  the  refracted  ray, 
MN  the  normal,  SAM  and  CAN 
the  angles  of  incidence  and  refrac- 
tion respectively.  Produce  ('A  back- 

Fio.  51.— REFRACTION.  "  ^v:ll'(l  *n  the  direction  AS:  8 A  >  is 
the  refraction.  An  observer  at  C  will 
see  the  star  S as  if  it  were  at  S.  AS'  is  the  apparent  direction  of 
the  ray  coming  from  the  star  S,  and  &  is  the  apparent  place  of  the  star 
as  affected  by  refraction. 

This  explanation  supposes  the  space  above  BE'  in  the 
figure  to  be  entirely  empty,  and  the  earth's  atmosphere, 
equally  dense  throughout,  to  fill  the  space  below  BB'. 
In  fact,  however,  the  earth's  atmosphere,  is  most  dense 
at  the  surface  of  the  earth,  and  gradually  diminishes  in 
density  to  its  exterior  boundary.  Therefore  we  must  sup- 
pose the  atmosphere  to  be  divided  into  a  great  number  of 
parallel  layers  of  air,  and  by  assuming  an  infinite  num- 
ber of  these  we  may  also  assume  that  throughout  each  one 
of  them  the  air  is  equally  dense.  Hence  the  preceding 
figure  will  only  represent  the  refraction  at  a  single  one  of 
these  layers.  The  path  of  a  ray  of  light  through  the  at- 
mosphere is  not  a  straight  line  like  A  C,  but  a  curve.  We 
may  suppose  this  curve  to  be  represented  in  Fig.  52,  where 


REFRACTION  AND  ABERRATION  OF  LIGHT.      171 

the  number  of  layers  has  been  taken  very  small  to  avoid 
confusing  the  drawing." 

Let  C  be  the  centre  and  A  a  point  of  the  surface  of  the 
earth;  let  S  be  a  star,  and  Sea,  ray  from  the  star  which  is 
refracted  at  the  various  layers  into  which  we  suppose  the 
atmosphere  to  be  divided,  and  which  finally  enters  the  eye 
of  an  observer  at  A  in  the  apparent  direction  S'A.  He 


FIG.  52.— REFRACTION  OP  LAYERS  OP  AIR. 

will  then  see  the  star  in  the  direction  S'  instead  of  that  of 
S9  and  SA  $',  the  refraction,  will  throw  the  star  nearer 
to  his  zenith  Z. 

The  angle  S'A  Z  is  the  apparent  zenith  distance  of  S; 
the  true  zenith  distance  of  S  is  Z  A  S,  and  SA  may  be 
assumed  to  coincide  with  S  e,  as  for  all  heavenly  bodies 
except  the  moon  it  practically  does.  The  line  Se  pro- 


172  ASTRONOMY. 

longed  will  meet  the  line  A  Z  in  a  point  above  A,  suppose 
aU'. 

Quantity  and  Effects  of  Refraction. — At  the  zenith  the 
refraction  is  0,  at  45°  zenith  distance  the  refraction  is  about 
1',  and  at  90°  it  is  34'  30";  that  is,  bodies  at  the  zenith 
distances  of  45°  and  90°  appear  elevated  above  their  true 
places  by  1'  and  34|'  respectively.  If  the  sun  has  just 
risen — that  is,  if  its  lower  limb  is  just  in  apparent  contact 
with  the  horizon — it  is  in  fact  entirely  below  the  true 
horizon,  for  the  refraction  (35')  has  elevated  its  centre  by 
more  than  its  whole  apparent  diameter  (32'). 

The  moon  is  full  when  it  is  exactly  opposite  the  sun, 
and  therefore,  were  there  no  atmosphere,  moon-rise  of  a 
full  moon  and  sunset  would  be  simultaneous.  In  fact, 
both  bodies  being  elevated  by  refraction,  we  see  the  full 
moon  risen  before  the  sun  has  set.  On  April  20th,  1837, 
the  full  moon  rose  eclipsed  before  the  sun  had  set. 

TWILIGHT. 

It  is  plain  that  one  effect  of  refraction  is  to  lengthen  the 
duration  of  daylight  by  causing  the  sun  to  appear  above 
the  horizon  before  the  time  of  his  geometrical  rising  and 
after  the  time  of  true  sunset. 

Daylight  is  also  prolonged  by  the  reflection  of  the  sun's 
rays  (after  sunset  and  before  sunrise)  from  the  small  parti- 
cles of  matter  suspended  in  the  atmosphere.  This  pro- 
duces a  general  though  faint  illumination  of  the  atmos- 
phere, just  as  the  light  scattered  from  the  floating  particles 
of  dust  illuminated  by  a  sunbeam  let  in  through  a  crack 
in  a  shutter  may  brighten  the  whole  of  a  darkened  room. 

The  sun's  direct  rays  do  not  reach  an  observer  on  the 


TWILIGHT.  173 

earth  after  the  instant  of  sunset,  since  the  solid  body  of 
the  earth  intercepts  them.  But  the  sun's  direct  rays 
illuminate  the  clouds  and  the  suspended  particles  of  the 
upper  air,  and  are  reflected  downwards  so  as  to  produce  a 
general  illumination  of  the  atmosphere. 

In  the  figure  let  A  B  CD  be  the  earth  and  A  an  observer 
on  its  surface,  to  whom  the  sun  S  is  just  setting.  A  a  is 
the  horizon  of  A;  El  of  B;  Cc  of  C;  DdofD.  Let  the 


FIG.  53. 

circle  P  Q  R  represent  the  upper  layer  of  the  atmosphere. 
Between  A  BCD  and  PQR  the  air  is  filled  with  sus- 
pended particles  which  will  reflect  light.  The  lowest  ray 
of  the  sun,  8  A  M,  just  grazes  the  earth  at  A  ;  the  higher 
rays  S  j^and  SO  strike  the  atmosphere  above  A  and  leave 
it  at  the  points  Q  and  R.  Each  of  the  lines  S  A  P  M, 
SQN,  is  bent  from  a  straight  course  by  refraction,  but 
S  R  0  is  not  bent  since  it  just  touches  the  upper  limits  of 


174  ASTROXOMY. 

the  atmosphere.  The  space  MABCDEia  the  earth's 
shadow.  An  observer  at  A  receives  the  (last)  direct  rays 
from  the  sun,  and  also  has  his  sky  illuminated  by  the  reflec- 
tion from  all  the  particles  lying  in  the  space  P  Q  Ji  T 
which  is  all  above  his  horizon  A  a. 

An  observer  at  B  receives  no  direct  rays  from  the  sun. 
It  is  after  sunset.  Nor  does  he  receive  any  light  from  all 
that  portion  of  the  atmosphere  below  A  P  M;  but  the  por- 
tion P  Rx,  which  lies  above  his  horizon  Bb,  is  lighted  by 
the  sun's  rays,  and  reflects  to  B  a  portion  of  the  incident 
rays. 

This  ttriliijht  is  strongest  at  R,  and  fades  away  gradu- 
ally toward  P.  The  altitude  of  the  twilight  is  I  d. 

To  an  observer  at  C  the  twilight  is  derived  from  the 
illumination  of  the  portion  PQz  which  lies  above  his 
horizon  Cc.  The  altitude  of  the  twilight  is  cd. 

To  an  observer  at  D  it  is  night.  All  of  the  illuminated 
atmosphere  is  below  his  horizon  Dd. 

The  student  should  notice  for  himself  the  twilight  arch 
which  appears  in  the  west  after  sunset.  It  is  more  marked 
in  summer  than  in  winter;  in  high  latitudes  than  in  low 
ones.  There  is  no  true  night  in  England  in  midsummer, 
for  example,  the  morning  twilight  beginning  before  the 
evening  twilight  has  ended  ;  and  in  the  torrid  zone  there 
is  no  perceptible  twilight.  Twilight  ends  when  the  sun 
reaches  a  point  20°  below  the  horizon. 

ABEBRATION  AND  THE  MOTION  OF  LIGHT. 

Besides  refraction,  there  is  another  cause  which  prevents 
our  seeing  the  celestial  bodies  exactly  in  the  true  direction 
in  which  they  lie  from  us;  namely,  the  progressive  mo- 
tion of  light.  We  see  objects  only  by  the  light  which 
emanates  from  them  and  reaches  our  eyes,  and  we  know 


REFRACTION  AND  ABERRATION  OF  LIGHT.      175 

that  this  light  requires  time  to  pass  over  the  space  which 
separates  us  from  the  luminous  object.  After  the  ray  of 
light  once  leaves  the  object,  the  latter  may  move  away,  or 
even  be  blotted  out  of  existence,  but  the  ray  of  light 
will  continue  on  its  course.  Consequently  when  we  look 
at  a  star,  we  do  not  see  the  star  that  now  is,  but  the  star 
that  was  several  years  ago.  If  it  should  be  annihilated,  we 
should  still  see  it  during  the  years  which  would  be  required 
for  the  last  ray  of  light  emitted  by  it  to  reach  us.  The 
velocity  of  light  is  so  great  that  in  all  observations  of  ter- 
restrial objects  our  vision  may  be  regarded  as  instantane- 
ous. But  in  celestial  observations  the  time  required  for 
the  light  to  reach  us  is  quite  appreciable  and  measurable. 

The  discovery  of  the  propagation  of  light  is  among  the 
most  remarkable  of  those  made  by  modern  science.  The 
fact  that  light  requires  time  to  travel  was  first  learned  by 
the  observations  of  the  satellites  of  Jupiter.  (See  Fig.  73.) 
Owing  to  the  great  magnitude  of  this  planet,  it  casts  a  much 
longer  and  larger  shadow  than  our  earth  does,  and  its  inner 
satellite  passes  throagh  this  shadow  and  is  eclipsed,  at  every 
revolution.  These  eclipses  can  be  observed  from  the  earth, 
the  satellite  vanishing  from  view  as  it  enters  the  shadow, 
and  reappearing  when  it  leaves  it  again.  The  astronomers 
of  the  seventeenth  century  made  a  careful  study  of  the  mo- 
tions of  these  bodies.  It  was,  however,  necessary  to  con- 
struct tables  by  which  the  times  of  the  eclipses  could  be  pre- 
dicted. It  was  found  by  EOEMEE  that  these  times  depended 
on  the  distance  of  Jupiter  from  the  earth.  If  he  made  his 
tables  agree  with  observations  when  the  earth  was  nearest 
Jupiter,  it  was  found  that  as  the  earth  receded  from  Jupiter 
in  its  annual  course  around  the  sun,  the  eclipses  were  con- 
stantly seen  later,  until,  when  at  its  greatest  distance,  the 


176  ASTRONOMY. 

times  appeared  to  be  22  minutes  late.  KOEMER  saw  that  it 
was  in  the  highest  degree  improbable  that  the  actual  motions 
of  the  satellites  should  be  affected  with  any  such  inequality; 
he  therefore  propounded  the  bold  theory  that  it  took  time 
for  light  to  come  from  Jupiter  to  the  earth.  The  extreme 
differences  in  the  times  of  the  eclipse  being  22  minutes,  he 
assigned  this  as  the  time  required  for  light  to  cross  the 
orbit  of  the  earth,  and  so  concluded  that  it  came  from  the 
sun  to  the  earth  in  11  minutes.  This  estimate  was  too 
great;  the  true  time  for  this  passage  being  about  8  minutes 
and  18  seconds. 

Discovery  of  Aberration. — This  theory  of  ROEMEK  was 
not  fully  accepted  by  his  contemporaries.  Hut  in  the  year 
1729  the  celebrated  BRADLEY,  afterward  Astnui'-iiK-r  Royal 
of  England,  discovered  a  phenomenon  of  an  entirely  dif- 
ferent character,  which  confirmed  the  theory,  lie  was 
then  engaged  in  making  observations  on  the  star  y  Dnt- 
conis  in  order  to  determine  its  parallax.  The  effect  of 
parallax  would  have  been  to  make  the  declination  of  the 
star  greatest  in  June  and  least  in  December,  while  in 
March  and  September  the  star  would  occupy  an  interme- 
diate or  mean  position.  But  the  result  was  entirely  dif- 
ferent. The  declinations  of  June  and  December  were  the 
same,  showing  no  effect  of  parallax;  but  instead  of  remain- 
ing constant  the  rest  of  the  year,  the  declination  was  some 
40  seconds  greater  in  September  than  in  March,  when  the 
effect  of  parallax  would  be  the  same.  This  showed  that 
the  direction  of  the  star  appeared  different,  not  according 
to  the  position  of  the  earth  in  its  orbit,  but  according  to 
the  direction  of  the  earth's  motion  around  the  sun,  the 
star  being  apparently  displaced  in  this  direction. 

To  show  how  this  is,  let  AB  be  the  optical  axis  of  a 


REFRACTION  AND  ABERRATION  OF  LIGHT.     177 

telescope,  and  8  a  star  from  which  emanates  a  ray  moving 
in  the  true  direction  SAB'.  Per- 
haps the  student  will  have  a  clearer 
conception  of  the  subject  if  he  imag- 
ines AB  to  be  a  rod  which  an  ob- 
server at  B  seeks  to  point  at  the  star 
8.  It  is  evident  that  he  will  point 
this  rod  in  such  a  way  that  the  ray 
of  light  shall  run  accurately  along  its 
length.  Suppose  now  that  the  ob- 
server is  moving  from  B  toward  B' 
with  such  a  velocity  that  he  moves  FIG.  54. 

from  B  to  B'  during  the  time  required  for  a  ray  of  light  to 
move  from  A  to  B'.  Suppose,  also,  that  the  ray  of  light 
8A  reaches  A  at  the  same  time  that  the  end  of  his  rod 
does.  Then  it  is  clear  that  while  the  rod  is  moving  from 
the  position  AB  to  the  position  A'B',  the  ray  of  light 
will  move  from  A  to  B' ,  and  will  therefore  run  accurately 
along  the  length  of  the  rod.  For  instance,  if  b  is  one  third 
of  the  way  from  B  to  B',  then  the  light,  at  the  instan^of 
the  rod  taking  the  position  b  a,  will  be  one  third  of  the  way 
from  A  to  B',  and  will  therefore  be  accurately  on  the  rod. 
Consequently,  to  the  observer,  the  rod  will  appear  to  be 
pointed  at  the  star.  In  reality,  however,  the  pointing  will 
not  be  in  the  true  direction  of  the  star,  but  will  deviate 
from  it  by  a  certain  angle  depending  upon  the  ratio  of  the 
velocity  with  which  the  observer  is  carried  along  to  the 
velocity  of  light.  This  presupposes  that  the  motion  of  the 
observer  is  at  right  angles  to  that  of  a  ray  of  light.  If 
this  is  not  his  direction,  we  must  resolve  his  velocity  into 
two  components,  one  at  right  angles  to  the  ray  and  one 
parallel  to  it.  The  latter  will  not  affect  the  apparent  di- 


178  ASTRONOMY. 

rection  of  the  star,  A  rich  will  therefore  depend  entirely 
upon  the  former. 

Effects  of  Aberration.— The  apparent  displacement  of 
the  heavenly  bodies  thus  produced  is  called  the  aberration 
of  light.  Its  effect  is  to  cause  each  of  the  fixed  stars  to 
describe  an  apparent  annual  oscillation  in  a  very  small  orbit. 
The  nature  of  the  displacement  may  he  conceived  of  in  the 
following  way:  Suppose  the  earth  at  any  moment,  in  the 
course  of  its  annual  revolution,  to  be  moving  toward  a 
point  of  the  celestial  sphere,  which  \ve  may  call  /'.  Then 
a  star  lying  in  the  direction  P  or  in  the  opposite  direction 
will  suffer  no  displacement  whatever.  A  star  lying  in  any 
other  direction  will  be  displaced  in  the  direction  of  the 
point  P  by  an  angle  depending  upon  its  angular  distance 
from  P.  At  90°  from  P  the  displacement  will  be  a  maxi- 
mum. 

Now,  if  the  star  lies  near  the  pole  of  the  ecliptic,  its  di- 
rection will  always  be  nearly  at  right  angles  to  the  direc- 
tion in  which  the  earth  is  moving.  A  little  consideration 
will  show  that  it  will  seem  to  describe  a  circle  in  conse- 
quence of  aberration.  If,  however,  it  lies  in  the  plane  of 
the  earth's  orbit,  then  the  various  points  toward  which  the 
earth  moves  in  the  course  of  the  year  all  lying  in  the  eclip- 
tic, and  the  star  being  in  this  same  plane,  the  apparent 
motion  will  be  an  oscillation  back  and  forth  in  this  plane, 
and  in  all  other  positions  the  apparent  motion  will  be  in  an 
ellipse  more  and  more  flattened  as  we  approach  the  ecliptic. 
The  maximum  displacement  of  a  star  by  aberration  is  20'. 44. 

The  connection  between  the  velocity  of  light  and  the  dis- 
tance of  the  sun  is  such  that  knowing  one  we  can  infer  the 
other.  Let  us  assume,  for  instance,  that  the  time  required 
for  light  to  reach  us  from  the  sun  is  498  seconds,  which 


REFRACTION  AND  ABERRATION  OF  LIGHT.      179 

is  probably  accurate  within  a  single  second.  Then  know- 
ing the  distance  of  the  sun,  we  may  obtain  the  velocity 
of  light  by  dividing  it  by  498.  But,  on  the  other  hand, 
if  we  can  determine  how  many  miles  light  moves  in  a 
second,  we  can  thence  infer  the  distance  of  the  sun  by 
multiplying  it  by  the  same  factor.  During  the  last  cen- 
tury the  distance  of  the  sun  was  found  to  be  certainly  be- 
tween 90  and  100  millions  of  miles.  It  was  therefore 
correctly  concluded  that  the  velocity  of  light  was  some- 
thing less  than  200,000  miles  per  second,  and  probably 
between  180,000  and  200,000.  This  velocity  has  since 
been  determined  more  exactly  by  the  direct  measurements 
at  the  surface  of  the  earth  already  mentioned. 


CHAPTER  XII. 
CHRONOLOGY. 

ASTRONOMICAL  MEASURES  OF  TIME. 

THE  int:mate  relation  of  astronomy  to  the  daily  life  of 
mankind  lias  arisen  from  its  affording  the  only  reliable  and 
accurate  measure  of  intervals  of  time.  The  fundamental 
units  of  time  in  all  ages  have  been  the  day,  the  month,  and 
the  year,  the  first  being  measured  by  the  revolution  of  the 
earth  on  its  axis,  the  second,  primitively,  by  that  of  the 
moon  around  the  earth,  and  the  third  by  that  of  the  earth 
round  the  sun. 

Of  the  three  units  of  time  just  mentioned,  the  most  nat- 
ural and  striking  is  the  shortest;  namely,  the  day.  It  is 
so  nearly  uniform  in  length  that  the  most  refined  astro- 
nomical observations  of  modern  times  have  never  certainly 
indicated  any  change.  This  uniformity,  and  its  entire 
freedom  from  all.  ambiguity  of  meaning,  have  always  made 
the  day  a  common  fundamental  unit  of  astronomers.  Ex- 
cept for  the  inconvenience  of  keeping  count  of  the  great 
number  of  days  between  remote  epochs,  no  greater  unit 
would  ever  have  been  necessary,  and  we  might  all  date  our 
letters  by  the  number  of  days  after  CHRIST,  or  after  any 
other  fixed  date. 

The  difficulty  of  remembering  great  numbers  is  such 
that  a  longer  unit  is  absolutely  necessary,  even  in  keeping 
the  reckoning  of  time  for  a  single  generation.  Such  a  unit 


CHRONOLOGY.  181 

is  the  year.  The  regular  changes  of  seasons  in  all  extra- 
tropical  latitudes  renders  this  unit  second  only  to  the  day 
in  the  prominence  with  which  it  must  have  struck  the 
minds  of  primitive  man.  These  changes  are,  however,  so 
slow  and  ill-marked  in  their  progress  that  it  would  have 
been  scarcely  possible  to  make  an  accurate  determination 
of  the  length  of  the  year  from  the  observation  of  the  sea- 
sons. Here  astronomical  observations  came  to  the  aid 
of  our  progenitors,  and,  before  the  beginnings  of  history, 
it  was  known  that  the  alternation  of  seasons  was  due  to 
the  varying  declination  of  the  sun,  as  the  latter  seemed 
to  perform  its  annual  course  among  the  stars  in  the 
"  oblique  circle"  or  ecliptic.  The  seasons  were  also  marked 
by  the  position  of  certain  bright  stars  relatively  to  the  sun; 
that  is,  by  those  stars  rising  or  setting  in  the  morning 
or  evening  twilight.  Thus  arose  two  methods  of  measur- 
ing the  length  of  the  year — the  one  by  the  time  when  the 
sun  crossed  the  equinoxes  or  solstices,  the  other  when  it 
seemed  to  pass  a  certain  point  among  the  stars.  As  we 
have  already  explained,  these  years  were  slightly  different, 
owing  to  the  precession  of  the  equinoxes,  the  first  or  equi- 
noctial year  being  a  little  less  and  the  second  or  sidereal 
year  a  little  greater  than  365|  days. 

The  number  01  days  in  a  year  is  too  great  to  admit  of 
their  being  easily  remembered  without  any  break;  an 
intermediate  period  is  therefore  necessary.  Such  a  period 
is  measured  by  the  revolution  of  the  moon  around  the 
earth,  or,  more  exactly,  by  the  recurrence  of  new  moon, 
which  takes  place,  on  the  average,  at  the  end  of  nearly 
29|  days.  The  nearest  round  number  to  this  is  30  days, 
and  12  periods  of  30  days  each  only  lack  5i  days  of  being 
a  year.  It  has  therefore  been  common  to  consider  a  year 


182  ASTRONOMY. 

as  made  up  of  12  months,  the  lack  of  exact  correspondence 
being  filled  by  various  alterations  of  the  length  of  the 
month  or  of  the  year,  or  by  adding  surplus  days  to  each 
year. 

The  true  lengths  of  the  day,  the  month,  and  the  year 
having  no  common  divisor,  a  difficulty  arises  in  attempting 
to  make  months  or  days  into  years,  or  days  into  months, 
owing  to  the  fractions  which  will  always  be  left  over.  At 
the  same  time,  some  rule  bearing  on  the  subject  is  neces- 
sary in  order  that  people  may  be  able  to  remember  the  year, 
month,  and  day.  Such  rules  are  found  by  choosing  some 
cycle  or  period  which  is  very  nearly  an  exact  number  of 
two  units,  of  months  and  of  days  for  example,  and  by 
dividing  this  cycle  up  as  evenly  as  possible. 

FOEMATION   OF   CALENDARS. 

The  months  now  or  heretofore  in  use  among  the  peoples  of  the 
globe  nwy  for  the  most  part  be  divided  into  two  classes: 

(1)  The  lunar  month  pure  and  simple,  or  the  mean  interval  be- 
tween successive  new  moons. 

(2)  An  approximation  to  the  twelfth  part  of  a  year,  without  respect 
to  the  motion  of  the  moon. 

The  Lunar  Month. — The  mean  interval  between  consecutive  new 
moons  being  nearly  29$  days,  it  was  common  in  the  use  of  the  pure 
lunar  month  to  have  months  of  29  and  30  <l;ivs  alternately.  This 
supposed  period,  however,  will  fall  short  by  a  day  in  about  2|  years. 
This  defect  was  remedied  by  introducing  cycles  containing  rather  more 
months  of  30  than  of  29  days,  the  small  excess  of  long  months  being 
spread  uniformly  through  the  cycle.  Thus  the  Greeks  had  a  cycle 
of  235  months,  of  which  125  were  full  or  long  mouths,  ;md  110  were 
short  or  deficient  ones.  We  see  that  the  length  of  this  cycle  was 
6940  days  (125  X  30  -f  110  X  29),  whereas  the  length  of  235  true  lunar 
months  is  235  X  29.53088  =  6939.688  days.  The  cycle  was  therefore 
too  long  by  less  than  one  third  of  a  day,  and  the  error  of  count  would 
amount  to  only  one  day  in  more  than  70  years.  The  Mohammedans, 
again,  took  a  cycle  of  360  months,  which  they  divided  into  169  short 
and  191  long  ones.  The  length  of  this  cycle  was  10631  days,  while 


CHRONOLOGY.  183 

the  true  length  of  360  lunar  months  is  10631.012  days.  The  count 
would  therefore  not  be  a  day  in  error  until  the  end  of  about  80 
cycles,  or  nearly  23  centuries.  This  month  therefore  follows  the 
moou  closely  enough  for  all  practical  purposes. 

Months  other  than  Lunar. — The  complications  of  the  system  just 
described,  and  the  consequent  difficulty  of  making  the  calendar 
month  represent  the  course  of  the  moon,  are  so  great  that  the  pure 
lunar  month  was  generally  abandoned,  except  among  people  whose 
religion  required  important  ceremonies  at  the  time  of  new  moon.  In 
such  cases  the  year  has  been  usually  divided  into  12  months  of 
slightly  different  lengths.  The  ancient  Egyptians,  however,  had  12 
mouths  of  30  days  each,  to  which  they  added  5  supplementary  days 
at  the  close  of  each  year. 

Kinds  of  Year. — As  we  find  two  different  systems  of  months  to 
have  been  used,  so  we  may  divide  the  calendar  years  into  three 
classes,  namely : 

(1)  The  lunar  year,  of  12  lunar  months. 

(2)  The  solar  year. 

(3)  The  combined  luni-solar  year. 

The  Lunar  Year. — We  have  already  called  attention  to  the  fact  that 
the  time  of  recurrence  of  the  year  is  not  well  marked  except  by 
astronomical  phenomena  which  the  casual  observer  would  hardly 
remark.  But  the  time  of  new  moon,  or  of  beginning  of  the  month, 
is  always  well  marked.  Consequently  it  was  very  natural  for  people 
to  begin  by  considering  the  year  as  made  up  of  twelve  lunations,  the 
error  of  eleven  days  being  unnoticeable  in  a  single  year  unless  care- 
ful astronomical  observations  were  made.  Even  when  this  error  was 
fully  recognized,  it  might  be  considered  better  to  use  the  regular 
year  of  12  lunar  months  than  to  use  one  of  an  irregular  or  varying 
number  of  months.  The  Mohammedans  use  such  a  year  to  this  day. 

The  Solar  Year.— In  forming  this  year,  the  attempt  to  measure  the 
year  by  revolutions  of  the  moon  is  entirely  abandoned,  and  its  length 
is  made  to  depend  entirely  on  the  change  of  the  seasons.  The  solar 
year  thus  indicated  is  that  most  used  in  both  ancient  and  modern 
times.  Its  length  has  been  known  to  be  nearly  365i  days  from  the 
times  of  the  earliest  astronomers,  and  the  system  adopted  in  our  cal- 
endar of  having  three  years  of  365  days  each,  followed  by  one  of  366 
days,  has  been  employed  in  China  from  the  remotest  historic  times. 
This  year  of  365J  days  is  now  called  by  us  the  Julian  Tear,  after 
JULIUS  C^SAR,  from  whom  we  obtained  it. 

The  Metonic  Cycle. — These  considerations  will  enable  us  to  under- 
stand the  origin  of  our  own  calendar.  We  begin  with  the  Metonic 
Cycle  of  the  ancient  Greeks,  which  still  regulates  some  religious  fes- 


184  ASTRONOMY. 

tivals,  although  it  has  disappeared  from  our  civil  reckoning  of  time. 
The  necessity  of  employing  lunar  months  caused  the  Greeks  great 
difficulty  in  regulating  their  calendar  so  as  to  accord  with  their  rules 
for  religious  feasts,  until  a  solution  of  the  problem  was  found  by 
METON,  about  433  B.C.  The  discovery  of  METON  was  that  u  period 
or  cycle  of  6940  days  could  be  divided  up  into  235  lunar  months,  and 
also  into  19  solar  years.  Of  these  months,  125  were  to  be  of  30  days 
each  and  110  of  29  days  each,  which  would,  in  all,  make  up  the  re- 
quired 6940  days.  To  see  how  nearly  this  rule  represents  the  actual 
motions  of  the  sun  and  moon,  we  remark  that: 

Days.  Hours.  Min. 

235  lunations  require 6939  16  31 

19  Julian  years  require 6939  18  0 

19  true  solar  years  require 6939  14  27 

We  see  that  though  the  cycle  of  6940  days  is  a  few  hours  too 
long,  yet  if  we  take  235  true  lunar  months,  we  find  their  whole  dura- 
tion to  be  a  little  less  than  19  Julian  years  of  365±  days  each,  and  a 
little  more  than  19  true  solar  years. 

The  problem  was  to  take  these  235  months  and  divide  them  up 
into  19  years,  of  which  12  should  have  12  months  each  and  7 
should  have  13  months  each.  The  long  years,  or  those  of  13  months, 
were  probably  those  corresponding  to  the  numl>ers  3,  5,  8,  11,  13,  16, 
and  19,  while  the  first,  second,  fourth,  sixth,  etc.,  were  short  years. 
In  general,  the  months  had  29  and  30  days  alternately,  but  it  was 
necessary  to  substitute  a  long  month  for  a  short  one  every  two  or 
three  years,  so  that  in  the  cycle  there  should  be  125  long  and  110 
short  months. 

Golden  Number. — This  is  simply  the  number  of  the  year  in  the 
Mrtonic  Cycle,  and  is  said  to  owe  its  appellation  to  the  enthusiasm 
of  the  Greeks  over  METON'S  discovery,  the  authorities  having  ordered 
the  division  and  numbering  of  the  years  in  the  new  calendar  to  be 
inscribed  on  public  monuments  in  letters  of  gold.  The  rule  for  find- 
ing the  golden  number  is  to  divide  the  number  of  the  year  by  19  and 
add  1  to  the  remainder.  From  1881  to  1899  it  may  be  found  by  sim- 
ply subtracting  1880  from  the  year.  It  is  employed  in  our  church 
calendar  for  finding  the  time  of  Easter  Sunday. 

The  Julian  Calendar. — The  civil  calendar  now  in  use  throughout 
Christendom  had  its  origin  among  the  Romans,  and  its  foundation 
was  laid  by  JULIUS  CESAR.  Before  his  time,  Rome  can  hardly  be 
said  to  have  had  a  chronological  system,  the  length  of  the  year  not 
being  prescribed  by  any  invariable  rule,  and  being  therefore  changed 
from  time  to  time  to  suit  the  caprice  or  to  compass  the  ends  of  the 


CHRONOLOGY.  185 

rulers.  Instances  of  this  tampering  disposition  are  familiar  to  the 
historical  student.  It  is  said,  for  instance,  that  the  Gauls  having  to 
pay  a  certain  monthly  tribute  to  the  Romans,  one  of  the  governors 
ordered  the  year  to  be  divided  into  14  months,  in  order  that  the  pay- 
days might  recur  more  rapidly.  A  year  was  fixed  at  365  days,  with 
the  addition  of  one  day  to  every  fourth  year.  The  old  Roman  months 
were  afterward  adjusted  to  the  Julian  year  in  such  a  way  as  to  give 
rise  to  the  somewhat  irregular  arrangement  of  months  which  we  now 
have. 

Old  and  New  Styles. — The  mean  length  of  the  Julian  year  is  365£ 
days,  about  Hi  minutes  greater  than  that  of  the  true  equinoctial 
year,  which  measures  the  recurrence  of  the  seasons.  This  difference 
is  of  little  practical  importance,  as  it  only  amounts  to  a  week  in  a 
thousand  years,  and  a  change  of  this  amount  in  that  period  is  pro- 
ductive of  no  inconvenience.  But,  desirous  to  have  the  year  as  cor- 
rect as  possible,  two  changes  were  introduced  into  the  calendar  by 
Pope  GREGORY  XIII.  with  this  object.  They  were  as  follows  : 

(1)  The  day  following  October  4,  1582,  was  called  the  15th  instead 
of  the  5th,  thus  advancing  the  count  10  days. 

(2)  The  closing  year  of  each  century,  1600,  1700,  etc.,  instead  of 
being  always  a  leap-year,  as  in  the  Julian  calendar,  is  such  only 
when  the  number  of  the  century  is  divisible  by  4.     Thus  while  1600 
remained  a  leap-year,  as  before,  1700,  1800,  and  1900  were  to  be 
common  years. 

This  change  in  the  calendar  was  speedily  adopted  by  all  Catholic 
countries,  and  more  slowly  by  Protestant  ones,  England  holding  out 
until  1752.  In  Russia  it  has  never  been  adopted  at  all,  the  Julian 
calendar  being  still  continued  without  change.  The  Russian  reckon- 
ing is  therefore  12  days  behind  ours,  the  ten  days  dropped  in  1582 
being  increased  by  the  days  dropped  from  the  years  1700  and  1800  in 
the  new  reckoning.  This  modified  calendar  is  called  the  Gregorian 
Calendar,  or  New  Style,  while  the  old  system  is  called  the  Julian 
Calendar,  or  Old  Style. 

It  is  to  be  remarked  that  the  practice  of  commencing  the  year  on 
January  1st  was  not  universal  until  comparatively  recent  times.  The 
most  common  times  of  commencing  were,  perhaps,  March  1st  and 
March  22d,  the  latter  being  the  time  of  the  vernal  equinox.  But 
January  1st  gradually  made  its  way,  and  became  universal  after  its 
adoption  by  England  in  1752. 

Solar  Cycle  and  Dominical  Letter. — In  our  church  calendars  Janu- 
ary 1st  is  marked  by  the  letter  A,  January  2d  by  B,  and  so  on  to  G, 
when  the  seven  letters  begin  over  again,  and  are  repeated  through 
the  year  in  the  same  order.  Each  letter  there  indicates  the  same  day 


186  ASTRONOMY. 

of  the  week  throughout  each  separate  year,  A  indicating  the  day  on 
which  January  1st  falls,  B  the  day  following,  and  so  on.  An  excep- 
tion occurs  in  leap  years,  when  February  29th  and  March  1st  are 
marked  by  the  same  letter,  so  that  a  change  occurs  at  the  beginning 
of  March.  The  letter  corresponding  to  Sunday  on  this  scheme  is 
called  the  Dominical  or  Sunday  letter,  and  when  we  once  know 
what  letter  it  is,  all  the  Sundays  of  the  year  are  indicated  by  that 
letter,  and  hence  all  the  other  days  of  the  week  by  their  letters.  In 
leap-years  there  will  be  two  Dominical  letters,  that  for  the  last  ten 
months  of  the  year  being  the  one  next  preceding  the  letter  for 
January  and  February.  In  the  Julian  calendar  the  Dominical  letter 
must  always  recur  at  the  end  of  28  years  (besides  three  recurrences 
at  unequal  intervals  in  the  me:m  time).  This  period  is  called  the 
solar  cycle,  and  determines  the  days  of  the  week  on  which  the  days 
of  the  month  fall  during  each  year. 

Since  any  day  of  any  year  occurs  one  day  later  in  the  week  than 
it  did  the  year  befon  .  <  r  two  days  later  when  a  29th  of  February 
has  intervened,  the  Dominical  letters  recur  in  the  order  G,  F,  E,  D, 
C,  B,  A,  G,  etc.  This  may  also  be  expressed  by  saying  that  any  day 
of  a  past  year  occurred  one  day  earlier  in  the  week  for  every  year 
that  has  elapsed,  and,  in  addition,  one  day  earlier  for  every  29th  of 
February  that  has  intervened.  This  fact  will  make  it  easy  to  calcu- 
late the  day  of  the  week  on  which  any  historical  event  happened 
from  the  day  corresponding  in  any  past  or  future  year.  Let  us  take 
the  following  example: 

On  what  day  of  the  week  was  WASHINGTON  born,  the  date  being 
1732,  February  22d,  knowing  that  February  22d,  1879,  fell  on 
Saturday?  The  interval  is  147  years:  dividing  by  4  we  have  a 
quotient  of  36  and  a  remainder  of  3,  showing  that,  had  every  fourth 
year  in  the  interval  been  a  leap  year,  there  were  either  36  or  37  leap- 
years.  As  a  February  29th  followed  only  a  week  after  the  date,  the 
number  must  be  37;*  but  as  1800  was  dropped  from  the  list  of  leap- 
years,  the  number  was  really  only  36.  Then  147  -f-  36  =  183  days 
advanced  in  the  week.  Dividing  by  7,  because  the  same  day  of  the 
week  recurs  after  seven  days,  we  find  a  remainder  of  1.  So 
February  22d,  1879,  is  one  day  further  advanced  than  was  Febru- 
ary 22d,  1732;  so  the  former  being  Saturday,  WASHINGTON  was  born 
on  Friday. 

*  Perhaps  the  most  convenient  way  of  deciding  whether  the  remainder  does 
or  does  not  indicate  an  additional  leap-year  is  to  subtract  it  from  the  last  date, 
and  see  whether  a  February  29th  then  intervenes.  Subtracting  3  years  from 
February  22d,  1879,  we  have  February  23d  1876,  and  a  29th  occurs  between  the 
two  dates,  only  a  week  after  the  first.  _ 


CHRONOLOGY.  187 


DIVISION  OF  THE  DAY. 

The  division  of  the  day  into  hours  was,  in  ancient  and  mediaeval 
times,  effected  in  a  way  very  different  from  that  which  we  practise. 
Artificial  time-keepers  not  being  in  general  use,  the  two  funda- 
mental moments  were  sunrise  and  sunset,  which  marked  the  day  as 
distinct  from  the  night.  The  first  subdivision  of  this  interval  was 
marked  by  the  instant  of  noon,  when  the  sun  was  on  the  meridian. 
The  day  was  thus  subdivided  into  two  parts.  The  night  was 
similarly  divided  by  the  times  of  rising  and  culmination  of  the 
various  constellations.  EURIPIDES  (480-407  B.C.)  makes  the  chorus 
in  RJiesus  ask : 

"  CHORUS.— Whose  is  the  guard?  Who  takes  my  turn?  The  first 
signs  are  setting,  and  the  sewn  Pleiades  are  in  the  sky,  and  the  Eagle 
glides  midway  through  heaven.  Awake!  Why  do  you  delay?  Awake 
from  your  beds  to  watch!  See  ye  not  the  brilliancy  of  the  moon? 
Morn,  morn  indeed  is  approaching,  and  hither  is  one  of  the  forewin- 
ning  stars" 

The  interval  between  sunrise  and  sunset  was  divided  into  twelve 
equal  parts  called  hours,  and  as  this  interval  varied  with  the  season, 
the  length  of  the  hour  varied  also.  The  night,  whether  long  or 
short,  was  divided  into  hours  of  the  same  character,  only  when  the 
night  hours  were  long  those  of  the  day  were  short,  and  vice  versa. 
These  variable  hours  were  called  temporary  hours.  At  the  time  of 
the  equinoxes  both  the  day  and  the  night  hours  were  of  the  same 
length  with  those  we  use;  namely,  the  twenty-fourth  part  of  the 
day ;  these  were  therefore  called  equinoctial  hours. 

Instead  of  commencing  the  civil  day  at  midnight,  as  we  do,  it  was 
customary  to  commence  it  at  sunset.  The  Jewish  Sabbath,  for 
instance,  commenced  as  soon  as  the  sun  set  on  Friday,  and  ended 
when  it  set  on  Saturday.  This  made  a  more  distinctive  division  of 
the  astronomical  day  than  that  which  we  employ,  and  led  naturally 
to  considering  the  day  and  the  night  as  two  distinct  periods,  each  to 
be  divided  into  12  hours. 

So  long  as  temporary  hours  were  used,  the  beginning  of  the  day 
and  the  beginning  of  the  night,  or,  as  we  should  call  it,  six  o'clock 
in  the  morning  and  six  o'clock  in  the  evening,  were  marked  by  the 
rising  and  setting  of  the  sun;  but  when  equinoctial  hours  were 
introduced,  neither  sunrise  nor  sunset  could  be  taken  to  count  from, 
because  both  varied  too  much  in  the  course  of  the  year.  It  therefore 
became  customary  to  count  from  noon,  or  the  time  at  which  the  sun 
passed  the  meridian.  The  old  habit  of  dividing  the  day  and  the 


188  ASTRONOMY. 

night  each  into  12  parts  was  continued,  the  first  12  being  reckoned 
from  midnight  to  noon,  and  the  second  from  noon  to  midnight.  The 
day  was  made  to  commence  at  midnight  rather  than  at  noon  for 
obvious  reasons  of  convenience,  although  noon  was  of  course  the 
point  at  which  the  time  had  to  be  determined. 

Equation  of  Time. — To  any  one  who  studied  the  annual  motion  of 
the  sun,  it  must  have  been  quite  evident  that  the  intervals  between 
its  successive  passages  over  the  meridian,  or  between  one  noon  and 
the  next,  could  not  be  the  same  throughout  the  year,  l>ecause  the 
apparent  motion  of  the  sun  in  right  ascension  is  not  constant.  It 
will  be  remembered  that  the  apparent  revolution  of  the  starry 
sphere,  or,  which  is  the  same  thing,  the  diurnal  revolution  of  the 
earth  upon  its  axis,  may  be  regarded  as  absolutely  constant  for  all 
practical  purposes.  This  revolution  is  measured  around  in  right 
ascension  as  explained  in  the  opening  chapter  of  this  work.  If  the 
sun  increased  its  right  ascension  by  the  same  amount  every  day,  it 
would  pass  the  meridian  3m  56"  later  every  day,  as  measured  by 
sidereal  time,  and  hence  the  intervals  between  successive  passages 
would  be  equal.  But  the  motion  of  the  sun  in  right  ascension  is 
unequal  from  two  causes:  (1)  the  unequal  motion  of  the  earth  in  its 
annual  revolution  around  it,  arising  from  the  eccentricity  of  the 
earth's  orbit,  and  (2)  the  obliquity  of  the  ecliptic.  How  the  first 
cause  produces  an  inequality  is  obvious.  The  mean  motion  is  3m  50* ; 
the  actual  motion  varies  from  3m  48*  to  4m  4s. 

The  effect  of  the  obliquity  of  the  ecliptic  is  still  greater.  When 
the  sun  is  near  the  equinox,  the  direction  of  its  motion  along  the 
ecliptic  makes  an  angle  of  2&J°  with  the  parallels  of  declination. 
Since  its  motion  in  right  ascension  is  measured  along  the  parallel  of 
declination,  we  see  that  it  is  less  than  the  motion  in  longitude.  The 
days  are  then  20  seconds  shorter  than  they  would  be  were  there  no 
obliquity.  At  the  solstices  the  opposite  effect  is  produced.  Here 
the  different  meridians  of  right  ascension  are  nearer  together  than 
they  are  at  the  equator;  when  the  sun  moves  through  one  degree 
along  the  ecliptic,  it  changes  its  right  ascension  by  1°-08;  here, 
therefore,  the  days  are  about  19  seconds  longer  than  they  would  be 
if  the  obliquity  of  the  ecliptic  were  zero. 

We  thus  have  to  recognize  two  slightly  different  kinds  of  days: 
solar  days  and  mean  days.  A  solar  day  is  the  interval  of  time 
between  two  successive  transits  of  the  sun  over  the  same  meridian, 
while  a  mean  day  is  the  mean  of  all  the  solar  days  in  a  year.  If  we 
had  two  clocks,  one  going  with  perfect  uniformity,  but  regulated 
so  as  to  keep  as  near  the  sun  as  possible,  and  the  other  changing  its 
rate  so  as  to  always  follow  the  sun,  the  latter  would  gain  or  lose  on 


CHRONOLOGY.  189 

the  former  by  amounts  sometimes  rising  to  22  seconds  in  a  day.  The 
accumulation  of  these  variations  through  a  period  of  several  months 
would  lead  to  such  deviations  that  the  sun-clock  would  be  14  minutes 
slower  than  the  other  during  the  first  half  of  February,  and  16 
minutes  faster  during  the  first  week  in  November.  The  time-keepers 
formerly  used  were  so  imperfect  that  these  inequalities  in  the  solar 
day  were  nearly  lost  in  the  necessary  irregularities  of  the  rate  of  the 
clock.  All  clocks  were  therefore  set  by  the  sun  as  often  as  was 
found  necessary  or  convenient.  But  during  the  last  century  it  was 
found  by  astronomers  that  the  use  of  units  of  time  varying  in  this 
way  led  to  much  inconvenience;  they  therefore  substituted  mean 
time  for  solar  or  apparent  time. 

Mean  time  is  so  measured  that  the  hours  and  days  shall  always  be 
of  the  same  length,  and  shall,  on  the  average,  be  as  much  behind  the 
sun  as  ahead  of  it.  We  may  imagine  a  fictitious  or  mean  sun  mov- 
ing along  the  equator  at  the  rate  of  3m  56*  in  right  ascension  every 
day.  Mean  time  will  then  be  measured  by  the  passage  of  this 
fictitious  sun  across  the  meridian.  Apparent  time  was  used  in 
ordinary  life  after  it  was  given  up  by  astronomers,  because  it  was 
very  easy  to  set  a  clock  from  time  to  time  as  the  sun  passed  a  noon- 
mark.  But  when  the  clock  was  so  far  improved  that  it  kept  much 
better  time  than  the  sun  did,  it  was  found  troublesome  to  keep  put- 
ting it  backward  and  forward  so  as  to  agree  with  the  sun.  Thus 
mean  time  was  gradually  introduced  for  all  the  purposes  of  ordinary 
life. 

The  common  household  almanac  should  give  the  equation  of  time, 
or  the  mean  time  at  which  the  sun  passes  the  meridian,  on  each  day 
of  the  year.  Then,  if  any  one  wishes  to  set  his  clock,  he  knows  the 
moment  when  the  sun  passes  the  meridian,  or  when  it  is  at  some  noon- 
mark,  and  sets  his  time-piece  accordingly.  For  all  purposes  where 
accurate  time  is  required,  recourse  must  be  had  to  astronomical 
observation.  It  is  now  customary  to  send  time-signals  every  day  at 
noon,  or  some  other  hour  agreed  upon,  from  observatories  along  the 
principal  lines  of  telegraph.  Thus  at  the  present  time  the  moment 
of  Washington  noon  is  signalled  to  New  York,  and  over  the  principal 
lines  of  railway  to  the  South  and  West.  Each  person  within  reach 
of  a  telegraph-office  can  then  determine  his  local  time  by  correcting 
these  signals  for  the  difference  of  longitude. 


PART  II. 

THE  SOLAR  SYSTEM  IN  DETAIL 


CHAPTER  I. 
STRUCTURE  OF  THE  SOLAR  SYSTEM. 

THE  solar  system  consists  of  the  sun  as  a  central  body, 
around  which  revolve  the  major  and  minor  planets,  with 
their  satellites,  a  iV\v  periodic  comets,  and  an  unknown 
number  of  meteor  swarms.  These  an.'  piM-manrnt  members 
of  the  system.  At  times  other  comets  appear,  and  move 
usually  in  parabolas  through  the  system,  around  the  sun, 
and  away  from  it  into  space  again,  thus  visiting  the  system 
without  being  permanent  members  of  it. 

The  bodies  of  the  system  may  be  classified  as  follows  : 

1.  The  central  body— the  Sun. 

2.  The  four  inner  planets — Mercury,  Venus,  the  Earth,  Mars. 

3.  A  group  of  small  planets,  sometimes  called  Asteroids,  revolving 
outside  of  the  orbit  of  Mars. 

4.  A  group  of  four  outer  planets — Jupiter,  Saturn,  Uranus,  and 
Neptune. 

5.  The  satellites,  or  secondary  bodies,  revolving  about  the  planets, 
their  primaries. 

6.  A  number  of  comets  and  meteor  swarms  revolving  in  very 
eccentric  orbits  about  the  sun. 

The  eight  planets  of  Groups  2  and  4  are  sometimes  classed  to- 
gether as  the  major  planet^  to  distinguish  them  from  the  two  hun- 
dred or  more  minor  plfineta  of  Group  3.  The  formal  definitions  of 
the  various  classes,  laid  down  by  Sir  WILLIAM  HERSCHEL  in  1802,  are 
worthy  of  repetition  : 


STRUCTURE  OF  THE  SOLAR 


^  SIT  I 


Planets  are  celestial  bodies  of  a  certain  very  considefat 
They  move  in  not  very  eccentric  ellipses  about  the  sun.  The  planes 
of  their  orbits  do  not  deviate  many  degrees  from  the  plane  of  the 
earth's  orbit.  Their  motion  about  the  sun  is  direct  (from  west  to 
east).  They  may  have  satellites  or  rings.  They  have  atmospheres  of 


FIG.  65.— RELATIVE  SURFACES  or  THE  PLANETS. 

considerable  extent,  which,  however,  bear  hardly  any  sensible  pro- 
portion to  their  diameters.  Their  orbits  are  at  certain  considerable 
distances  from  each  other. 

Asteroids,  now  more  generally  known  as  small  or  minor  planet*,  are 
celestial  bodies  which  move  about  the  sun  }n  orbits,  either  of  little  or 


192 


ASTROXOMY. 


of  considerable  eccentricity,  the  planes  of  which  orbits  may  be  in- 
clined to  the  ecliptic  at  any  angle  whatsoever.  They  may  or  may 
not  have  considerable  atmospheres. 

Cometi  are  celestial  bodies,  generally  of  a  very  small  mass,  though 
how  far  this  may  be  limited  is  yet  unknown.     They  move  in  very 


Fio.  56.— APPARENT  MAGNITUDES  OF  THE  SUN  AS  SEEN  FROM  DIFFERENT  PLANETS. 

eccentric  ellipses  or  in  parabolic  arcs  about  the  tun.  The  planes  of 
their  motion  admit  of  the  greatest  variety  in  their  situation.  The 
direction  of  their  motion  is  also  totally  undetermined.  They  have 
atmospheres  of  very  great  extent,  which  show  themselves  in  various 
forms  us  tails,  coma,  haziness,  etc. 


STRUCTURE  OF  THE  SOLAR  SYSTEM. 


193 


Relative  Surfaces  of  the  Planets.— The  comparative  surfaces  of  the 
major  planets,  as  they  would  appear  to  an  observer  situated  at  an 
equal  distance  from  all  of  them,  is  given  in  the  figure  on  page  191. 

The  relative  apparent  magnitudes  of  the  sun,  as  seen  from  the 
various  planets,  is  shown  in  the  figure  on  page  192. 

Flora  and  Mnemosyne  are  two  of  the  asteroids. 

A  curious  relation  between  the  distances  of  the  planets,  known  as 
BODE'S  law,  deserves  mention.     If  to  the  numbers 
0,  3,  6,  12,  24,  48,  96,  192,  384, 

each  of  which  (the  second  excepted)  is  twice  the  preceding,  we  add 
4,  we  obtain  the  series 

4,  7,  10,  16,  28,  52,  100,  196,  388. 

These  last  numbers  represent  approximately  the  distances  of  the 
planets  from  the  sun  (except  for  Neptune,  which  was  not  discovered 
when  the  so-called  law  was  announced). 

This  is  shown  in  the  following  table  : 


PLANETS. 

Actual 
Distance. 

BODE'S  Law. 

3-9 

4-0 

Venus 

7-2 

7-0 

Earth 

10-0 

10-0 

Mars                               

15-2 

16-0 

[Ceres]     

27-7 

28-0 

Jupiter  

52-0 

52-0 

Saturn 

95-4 

100-0 

,  Uranus 

191-8 

96-0 

^Neptune     .... 

300-4 

888  0 

It  will  be  observed  that  Neptune  does  not  fall  within  this  ingenious 
scheme.  Ceres  is  one  of  the  minor  planets. 

The  relative  brightness  of  the  sun  and  the  various  planets  has  been 
measured  by  ZOLLNER,  and  the  results  are  given  below.  The  column 
per  cent  shows  the  percentage  of  error  indicated  in  the  separate  re- 
sults: 


SUN  AND 

Ratio  :  1  to 

Percent,  of  Error. 

Moon             

618  000 

1-6 

6  994  000  000 

5-8 

5  472  000  000 

5-7 

Saturn  (ball  alone) 

130  980  000  000 

5-0 

8,486,000,000,000 

6-0 

Neptune  

79  620  000  000  000 

5-5 

194 


ASTRONOMY. 


The  differences  in  the  density,  size,  mass,  and  distance  of  the 
several  planets,  and  in  the  amount  of  solar  light  and  heat  which  they 
receive,  are  immense.  The  distance  of  Neptune  is  eighty  times  that 
of  Mercury,  and  it  receives  only  ^^  as  much  light  and  heat  from  the 
sun.  The  density  of  the  earth  is  about  six  times  that  of  water,  while 
Saturn's  mean  density  is  less  than  that  of  water. 

The  mass  of  the  sun  is  far  greater  than  that  of  any  single  planet 
in  the  system,  or  indeed  than  the  combined  mass  of  all  of  them.  In 
general,  it  is  a  remarkable  fact  that  the  mass  of  any  given  planet  ex- 
ceeds the  sum  of  the  masses  of  all  the  planets  of  less  mass  than  itself. 
This  is  shown  in  the  following  table,  where  the  masses  of  the  planets 
are  taken  as  fractions  of  the  sun's  mass,  which  we  here  express  as 
1,000,000,000: 


900 


324 


3,000 


51,000    885,580    954,905  1,000,000,000   Masses. 


PLANETS 


The  total  mass  of  the  small  planets,  like  their  number,  is  unknown, 
but  it  is  probably  less  than  one  th<>M-:imltli  that  of  our  earth,  and 
would  hardly  increase  the  sum-total  of  the  above  masses  of  the  solar 
system  hy  more  than  one  or  two  units.  Tin-  sun's  mass  is  thus  over 
TOO  times  that  of  all  the  other  bodies,  and  hence  the  fact  of  its  cen- 
tral position  in  the  solar  system  is  explained.  In  fact,  the  centre  of 
gratify  ot  the  whole  solar  system  is  very  little  outside  the  body  of  the 
sun,  and  will  be  inside  of  it  when  J>i]>it<:r  and  Saturn  are  in  opposite 
directions  from  it. 

Planetary  Aspects. — The  motions  of  the  planets  about  the  sun  have 
been  explained  in  Chapter  V.  From  what  is  there  said  it  appears 
that  the  best  time  to  see  one  of  the  "outer  planets  will  be  when  it  is 
in  opposition;  that  is,  when  its  geocentric  longitude  or  its  right  as- 
cension differs  180°  or  12h  from  that  of  the  sun.  At  such  a  time  the 
planet  will  rise  at  sunset  and  culminate  at  midnight.  During  the 
three  months  following  opposition  the  planet  will  rise  from  three  to 
six  minutes  earlier  every  day,  so  that,  knowing  when  a  planet  is  in 
opposition,  it  is  easy  to  find  it  at  any  other  time.  For  example,  a 
month  after  opposition  the  planet  will  be  two  or  three  hours  high 
about  sunset,  and  will  culminate  about  nine  or  ten  o'clock.  Of 
course  the  inner  planets  never  come  into  opposition,  and  hence  are 
best  seen  about  the  times  of  their  greatest  elongations. 


STRUCTURE  OF  THE  SOLAR  81' STEM. 


195 


Dimensions  of  the  Solar  System. — The  figure  gives  a  rough  plan  of 
part  of  the  solar  system  as  it  would  appear  to  a  spectator  immediately 
above  or  below  the  plane  of  the  ecliptic.  It  is  drawn  approximately 
to  scale,  the  mean  distance  of  the  earth  (=  1)  being  half  an  inch. 
The  mean  distance  of  Saturn  would  be  4-77  inches,  of  Uranus  9-59 


FIG.  57. 


inches,  of  Neptune  15-03  inches.     On  the  same  scale  the  distance  of 
the  nearest  fixed  star  would  be  103,133  inches,  or  over  one  and  one  half 
miles. 
The  arrangement  of  the  planets  and  satellites  is,  then — 


The  Inner  Group. 
Mercury. 
Venus. 

Earth  and  Moon. 
Mars  and  2  moons. 


Asteroids. 

200  minor  planets, 

and    probably 

many  more. 


The  Outer  Group. 
/  Jupiter  and  4  moons. 
J  Saturn  and  8  moons. 
J  Uranus  and  4  moons. 
(  Neptune  and  1  moon. 


196  ASTRONOMY. 

To  avoid  repetitions,  the  elements  of  the  major  planets  and  other 
data  are  collected  into  the  two  following  tables,  to  which  reference 
should  be  made  by  the  student.  The  units  in  termsof  which  Hie  vari- 
ous  quantities  are  given  are  those  familiar  to  us,  as  miles,  days,  etc., 
yet  some  of  the  distances,  etc.,  are  so  immensely  greater  than  any 
known  to  our  daily  experience  that  we  must  have  recourse  to  illus- 
trations to  obtain  any  idea  of  them  at  all.  For  example,  the  dis- 
tance of  the  sun  is  said  to  be  92*  million  miles.  It  is  of  importance 
that  some  idea  should  !><•  had  of  this  distance,  as  it  is  the  unit,  in 
terms  of  which  not  only  the  distances  in  the  sohir  system  are  ex- 
pressed, but  which  serves  as  a  basis  for  measures  in  the  stellar  uni- 
verse. Thus  when  we  say  that  the  distance  of  the  nearext  star  is  over 
200,000  times  the  mean  distance  e.f  tin-  sun,  it  becomes  necessary  to  see 
if  some  conception  can  be  obtained  of  one  factor  in  this.  Of  the  ab- 
stract number,  92,500,000.  we  have  no  conception.  It  is  far  too 
great  for  us  to  have  counted.  We  have  never  taken  in  at  one  view 
even  a  million  similar  discrete  objects.  The  largest  tree  has  less 
than  500,000  leaves.  To  count  from  1  to  200  requires  with  very 
rapid  counting,  60  seconds.  Suppose  this  kept  up  for  a  day  without 
intermission  ;  at  the  end  we  should  have  counted  288.000,  which  is 
about  ,Jff  of  92,500,000.  Hence  over  10  months'  uninterrupted 
counting  by  night  and  day  would  l>e  required  simply  to  enumerate 
the  number,  and  long  before  the  expiration  of  the  task  all  idea  of  it 
would  have  vanished  We  may  take  other  and  perhaps  more  strik- 
ing examples.  We  know,  for  instance,  that  the  time  of  the  fastest 
express-trains  between  New  York  and  Chicago,  \\hich  average  40 
miles  per  hour,  is  about  a  day.  Suppose  such  a  train  to  start  for  the 
sun  and  to  continue  running  at  this  rapid  rate.  It  would  take  363 
years  for  the  journey.  Three  hundred  and  sixty-three  years  ago  there 
was  not  a  European  settlement  in  America. 

A  cannon-ball  moving  continuously  across  the  intervening  space 
nt  its  highest  speed  would  require  about  nine  years  to  reach  the  sun. 
The  report  of  the  cannon,  if  it  could  be  conveyed  to  the  sun  with 
the  velocity  of  sound  in  air,  would  arrive  there  five  years  after  the 
projectile.  Such  a  distance  is  entirely  inconceivable,  and  yet  it  is 
only  a  small  fraction  of  those  with  which  astronomy  has  to  deal,  even 
in  our  own  system.  The  distance  of  Neptune  is  30  times  as  great. 

If  we  examine  the  dimensions  of  the  various  orbs,  we  meet  almost 
equally  inconceivable  numbers.  The  diameter  of  the  sun  is  860.000 
miles;  its  radius  is  but  430,000,  and  yet  this  is  nearly  twice  the  mean 
distance  of  the  moon  from  the  enrth.  Try  to  conceive,  in  looking  at 
the  moon  in  a  clear  sky,  that  if  the  centre  of  the  sun  could  be  placed 
at  the  centre  of  the  earth,  the  moon  would  be  far  within  the  sun's 


STRUCTURE  OF  THE  SOLAR  SYSTEM.  197 

surface.  Or  again,  conceive  of  the  force  of  gravity  at  the  surface  of 
the  various  bodies  of  the  system.  At  the  sun  it  is  nearly  28  times 
that  known  to  us.  A  pendulum  beating  seconds  here  would,  if 
transported  to  the  sun  vibrate  with  a  motion  more  rapid  than  that 
of  a  watch-balance.  The  muscles  of  the  strongest  man  would  not 
support  him  erect  on  the  surface  of  the  sun :  even  lying  down  he 
would  crush  himself  to  death  under  his  own  weight  of  two  tons. 
We  may  by  these  illustrations  get  some  rough  idea  of  the  meaning  of 
the  numbers  in  these  tables,  :md  of  the  incapability  of  our  limited 
ideas  to  comprehend  the  true  dimensions  of  even  the  solar  system. 


198 


ASTRONOMY. 


STRUCTURE  OF  THE  SOLAR  SYSTEM. 


199 


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CHAPTER  H. 

THE  SUN. 

GENERAL  SUMMARY. 

To  enable  the  nature  of  the  phenomena  of  the  sun  to  be 
clearly  understood,  we  preface  our  account  of  its  physical 
constitution  by  a  brief  summary  of  its  main  features. 

Photosphere. — To  the  simple  vision  the  sun  presents  the 
aspect  of  a  brilliant  sphere.  The  visible  shining  surface 
of  this  sphere  is  called  the  photosphere,  to  distinguish  it 
from  the  body  of  the  sun  as  a  whole.  The  apparently  flat 
surface  presented  by  a  view  of  the  photosphere  is  called  the 
sun's  disk. 

Spots. — When  the  photosphere  is  examined  with  a  tele- 
scope, small  dark  patches  of  varied  and  irregular  outline 
are  frequently  found  upon  it.  These  are  called  the  *olar 
spots. 

Rotation. — "When  the  spots  are  observed  from  day  to 
day,  they  are  found  to  move  over  the  sun's  disk  from  east  to 
west  in  such  a  way  as  to  show  that  the  sun  rotates  on  its 
axis  in  a  period  of  "25  or  2G  days.  The  sun,  therefore,  has 
axis,  poles,  and  equator,  like  the  earth,  the  axis  being  the 
line  around  which  it  rotates  from  west  to  east. 

Facnlae.—  Groups  of  minute  specks  brighter  than  the 
general  surface  of  the  sun  are  often  seen  in  the  neighbor- 
hood of  spots  or  elsewhere.  They  are  called  faculce. 


THE  kUN.  201 

Chromosphere,  or  Sierra. — The  solar  photosphere  is  cov- 
ered by  a  layer  of  glowing  vapors  and  gases  of  very  irregu- 
lar depth.  At  the  bottom  lie  the  vapors  of  many  metals, 
iron,  etc.,  volatilized  by  the  fervent  heat  which  reigns 
there,  while  the  ripper  portions  are  composed  principally 
of  hydrogen  gas.  This  vaporous  atmosphere  is  commonly 
called  the  chromosphere,  sometimes  the  sierra.  It  is  en- 
tirely invisible  to  direct  vision,  whether  with  the  telescope 
or  naked  eye,  except  for  a  few  seconds  about  the  beginning 
or  end  of  a  total  eclipse,  but  it  may  be  seen  on  any  clear 
day  through  the  spectroscope. 

Prominences,  Protuberances,  or  Red  Flames. — The  gases 
of  the  chromosphere  are  frequently  thrown  up  in  irregular 
masses  to  vast  heights  above  the  photosphere,  it  may  be 
50,000,  100,000,  or  even  200,000  kilometres.  Like  the 
chromosphere,  these  masses  have  to  be  studied  with  the 
spectroscope,  and  can  never  be  directly  seen  except  when 
the  sunlight  is  cut  off  by  the  intervention  of  the  moon 
during  a  total  eclipse.  They  are  then  seen  as  rose-colored 
flames,  or  piles  of  bright  red  clouds  of  irregular  and  fantas- 
tic shapes. 

Corona. — During  total  eclipses  the  sun  is  seen  to  be  en- 
veloped by  a  mass  of  soft  white  light,  much  fainter  than 
the  chromosphere,  and  extending  out  on  all  sides  far  be- 
yond the  highest  prominences.  It  is  brightest  around  the 
edge  of  the  sun,  and  fades  off  toward  its  outer  boundary, 
by  insensible  gradations.  This  halo  of  light  is  called  the 
corona,  and  is  a  very  striking  object  during  a  total  eclipse. 

THE  PHOTOSPHERE. 

Aspect  and  Structure  of  the  Photosphere. — The  disk  of  the  snn  is  cir- 
cular in  shape,  no  matter  what  side  of  the  sun's  globe  is  turned  to- 


202 


ASTRONOMY. 


ward  us,  whence  it  follows  that  the  sun  itself  is  a  sphere.  The  aspect 
of  the  disk,  when  viewed  with  the  naked  eye,  or  with  a  telescope  of 
low  power,  is  that  of  a  uniform  bright,  shining  surface,  hence  called 
the  photosphere.  With  a  telescope  of  higher  power  the  photosphere 
is  seen  to  be  diversified  with  groups  of  spots,  and  under  good  con- 


:•    t\*\"l?*&''£ +'****<  *  *."»•' ;**' 

1   • 

; 


»•  ! 


;W«: 


Fia.  68.— RETICULATED  ARRANGEMENT  OF  THE  SUN'S  PHOTOSPHERE. 
(From  a  photograph.) 

ditions  the  whole  mass  has  a  mottled  or  curdled  appearance.  This 
mottling  is  caused  by  the  presence  of  cloud-like  forms,  whose  out- 
lines though  faint  are  yet  distinguishable.  The  background  is  also 
covered  with  small  white  clots  or  forms  still  smaller  than  the  clouds. 


THE  SUN.  203 

These  are  the  "rice-grains,"  so  called.  The  clouds  themselves  are 
composed  of  small,  intensely  bright  bodies,  irregularly  distributed, 
of  tolerably  definite  shapes,  which  seem  to  be  suspended  in  or  super- 
posed on  a  darker  medium  or  background.  The  spaces  between  the 
bright  dots  vary  in  diameter  from  2"  to  4"  (about  1400  to  2800  kilo- 
metres). The  rice-grains  themselves  have  been  seen  to  be  composed 
of  smaller  granules,  sometimes  not  more  than  0".3  (135  miles)  in 
diameter,  clustered  together.  Thus  there  have  been  seen  at  least 
three  orders  of  aggregation  in  the  brighter  parts  of  the  photosphere: 
the  larger  cloud-like  forms;  the  rice-grains;  and,  smallest  of  all,  the 
granules. 

Light  and  Heat  from  the  Photosphere, — The  photosphere 
is  not  equally  bright  all  over  the  apparent  disk.  This  is  at 
once  evident  to  the  eye  in  observing  the  sun  with  a  tele- 
scope. The  centre  of  the  disk  is  most  brilliant,  and  the 
edges  or  limbs  are  shaded  off  so  as  to  forcibly  suggest  the 
idea  of  an  absorptive  atmosphere,  which,  in  fact,  is  the 
cause  of  this  appearance. 

Such  absorption  occurs  not  only  for  the  rays  by  which 
we  see  the  sun,  the  so-called  visual  rays,  but  for  those 
which  have  the  most  powerful  effect  in  decomposing  the 
salts  of  silver,  the  so-called  chemical  rays,  by  which  the 
ordinary  photograph  is  taken. 

The  amount  of  heat  received  from  different  portions  of 
the  sun's  disk  is  also  variable,  according  to  the  part  of  the 
apparent  disk  examined.  This  is  what  we  should  expect. 
That  is,  if  the  intensity  of  any  one  of  these  radiations  (as 
felt  at  the  earth)  varies  from  centre  to  circumference,  that 
of  every  other  should  also  vary,  since  they  are  all  modifi- 
cations of  the  same  primitive  motion  of  the  sun's  con- 
stituent particles.  But  the  constitution  of  the  sun's  at- 
mosphere  is  such,  that  the  law  of  variation  for  the  three 
classes  is  different.  The  intensity  of  the  radiation  in  the 
sun  itself  and  inside  of  the  absorptive  atmosphere  is  prob- 


204  ASTRONOMT. 

ably  nearly  constant.  The  ray  which  leaves  the  centre 
of  the  sun's  disk  in  passing  to  the  earth  traverses  the 
smallest  possible  thickness  of  the  solar  atmosphere,  while 
the  rays  from  points  of  the  sun's  body  which  appear  to  us 
near  the  limbs  pass,  on  the  contrary,  through  the  maxi- 
mum thickness  of  atmosphere,  and  are  thus  longest  sub- 
jected to  its  absorptive  action. 

This  is  plainly  a  rational  explanation,  since  the  part  of 
the  sun  which  is  seen  by  us  as  the  limb  varies  with  the 
position  of  the  earth  in  its  orbit  and  with  the  position  of 
the  sun's  surface  in  its  rotation,  and  has  itself  no  physical 
peculiarity.  The  various  absorptions  of  different  (-hisses 
of  rays  correspond  to  this  supposition,  the  more  refrangi- 
ble rays,  violet  and  blue,  suffering  most  absorption,  as  they 
must  do,  being  composed  of  waves  of  shorter  wave-length. 

Amount  of  Heat  Emitted  by  the  Sun. — Owing  to  the 
absorption  of  the  solar  atmosphere,  it  follows  that  we  re- 
ceive only  a  portion — perhaps  a  very  small  portion — of 
the  rays  emitted  by  the  sun's  photosphere. 

If  the  sun  had  no  absorptive  atmosphere,  it  would  seem 
to  us  hotter,  brighter,  and  more  blue  in  color. 

Exact  notions  as  to  how  great  this  absorption  is  are  hard 
to  gain,  but  it  maybe  said  roughly  that  the  best  authorities 
agree  that  although  it  is  quite  possible  that  the  sun's  at- 
mosphere absorbs  half  the  emitted  rays,  it  probably  does 
not  absorb  four  fifths  of  them. 

The  amount  of  this  absorption  is  a  practical  question  to 
us  on  the  earth.  So  long  as  the  central  body  of  the  sun 
continues  to  emit  the  same  quantity  of  rays,  it  is  plain  that 
the  thickness  of  the  solar  atmosphere  determines  the  num- 
ber of  such  rays  reaching  the  earth.  If  in  former  times 
this  atmosphere  was  much  thicker,  then  less  heat  would 


THE  SUN.  205 

have  reached  the  earth.  Glacial  epochs  may  be  explained 
in  this  way.  If  the  central  body  of  the  sun  has  likewise 
had  different  emissive  powers  at  different  times,  this  again 
would  produce  a  variation  in  the  temperature  of  the  earth. 

Amount  of  Heat  Radiated. — There  is  at  present  no  way  of  determin- 
ing accurately  either  the  absolute  amount  of  heat  emitted  from  the 
central  body  or  the  amount  of  this  heat  stopped  by  the  solar  atmos- 
phere itself.  All  that  can  be  done  is  to  measure  (and  that  only 
roughly)  the  amount  of  heat  really  received  by  the  earth,  without 
attempting  to  define  accurately  the  circumstances  which  this  radiation 
has  undergone  before  reaching  the  earth. 

POUILLET  has  experimented  upon  this  question,  making  allowance 
for  the  time  that  the  sun  is  below  the  horizon  of  any  place,  and  for 
the  fact  that  the  solar  rays  do  not  in  general  strike  perpendicularly 
but  obliquely  upon  any  given  part  of  the  earth's  surface.  His  con- 
clusions may  be  stated  as  follows  :  if  our  own  atmosphere  were  re- 
moved, the  solar  rays  would  have  energy  enough  to  melt  a  layer  of 
ice  9  centimetres  thick  over  the  whole  earth  daily,  or  a  layer  of  about 
32  metres  thick  in  a  year. 

This  action  is  constantly  at  work  over  the  whole  of  the  sun's  sur- 
face. To  produce  a  similar  effect  by  the  combustion  of  coal  would 
require  that  a  layer  of  coal  5  metres  thick  spread  all  over  the  sun 
should  be  consumed  every  hour.  This  is  equivalent  to  a  continuous 
evolution  of  10,000  horse-power  on  every  square  foot  of  the  sun's 
surface.  If  the  sun  were  of  solid  coal  and  produced  its  own  heat  by 
combustion,  it  would  burn  out  in  6000  years. 

Of  this  enormous  outflow  of  heat  the  earth  receives  only 
FSOOO^OOOO-  We  have  expressed  the  power  of  even  this  small  frac- 
tion of  the  sun's  heat  in  terms  of  the  ice  it  would  melt  daily.  If  we 
compute  how  much  coal  it  would  require  to  melt  the  same  amount, 
and  then  further  calculate  how  much  work  this  coal  would  do,  we 
shall  find  that  the  sun  sends  to  the  earth  an  amount  of  heat  which  is 
equivalent  to  one  horse-power  continuously  acting  for  every  30 
square  feet  of  the  earth's  surface.  Most  of  this  is  expended  in  main- 
taining the  earth's  temperature;  but  a  small  portion,  about  yg^rr*  is 
stored  away  by  animals  and  vegetables,  and  this  slight  fraction  is 
the  source  upon  which  the  human  race  depends.  If  this  were  with- 
drawn the  race  would  perish. 

Of  the  total  amount  of  heat  radiated  by  the  sun  the  earth  receives 
but  an  insignificant  share.  The  sun  is  capable  of  heating  the  entire 
surface  of  a  sphere  whose  radius  is  the  earth's  mean  distance  to  the 


206  ASTHONOMY. 

same  degree  that  the  earth  is  now  heated.  The  surface  of  such  a 
sphere  is  2,170,000,000  times  greater  than  the  angular  dimensions  of 
the  earth  as  seen  from  the  sun,  and  hence  the  earth  receives  less  than 
one  two-billionth  part  of  the  solar  radiation.  The  rest  of  the  solar 
rays  are,  so  far  as  we  know,  lost  in  spun-. 

Solar  Temperature. — From  the  amount  of  heat  actually  radiated  by 
the  sun,  attempts  have  been  made  to  determine  the  actual  tempera- 
ture of  the  solar  surface.  The  estimates  reached  by  various  authori- 
ties differ  widely,  as  the  laws  which  govern  the  absorption  within 
the  solar  envelope  are  almost  unknown.  Some  such  law  of  absorp- 
tion has  to  be  supposed  in  any  such  investigation,  and  the  estimates 
have  differed  widely  according  to  the  adopted  law. 

SKCCHI  e>timates  this  temperature  at  about  6,100,000°  C.  Other 
estimates  are  far  lower,  but,  according  to  all  sound  philosophy,  the 
temperature  must  far  exceed  any  terrestrial  temperature.  There  can 
be  no  doubt  that  if  the  temperature  of  the  earth's  surface  were  sud- 
denly raised  to  that  of  the  sun,  no  single  chemical  element  would  re- 
main in  its  present  condition.  The  most  refractory  materials  would 
be  at  once  volatili/.ed. 

We  may  concentrate  the  heat  received  upon  several  square  feet 
(the  surface  of  a  huge  burning-lens  or  mirror,  for  instance),  examine 
its  effects  at  the  focus,  and,  making  allowance  for  the  condensation 
by  the  lens,  see  what  is  the  minimum  possible  temperature  of  the 
sun.  The  temperature  at  the  focus  of  the  lens  cannot  be  higher  than 
that  of  the  source  of  heat  in  the  sun ;  we  can  only  concentrate  the 
heat  received  on  the  surface  of  the  lens  to  one  point  and  examine  its 
effects.  If  a  lens  three  feet  in  diameter  be  used,  the  most  refractory 
materials,  as  fire-clay,  platinum,  the  diamond,  are  at  once  melted  or 
volatilized.  The  effect  of  the  lens  is  plainly  the  same  as  if  the  earth 
were  brought  closer  to  the  sun,  in  the  ratio  of  the  diameter  of  the 
focal  image  to  that  of  the  lens.  In  the  case  of  the  lens  of  three  feet, 
allowing  for  the  absorption,  etc.,  this  distance  is  yet  greater  than 
that  of  the  moon  from  the  earth,  so  that  it  appears  that  any  comet  or 
planet  so  close  as  this  to  the  sun,  if  composed  of  materials  similar  to 
those  in  the  earth,  must  be  vaporized. 

SUN-SPOTS  AND  FACULJE. 

A  very  cursory  examination  of  the  sun's  disk  with  a  small  tele- 
scope will  generally  show  one  or  more  dark  spots  upon  the  photo- 
sphere. These  are  of  various  sizes,  from  minute  black  dots  1"  or  2* 
in  diameter  (1000  kilometres  or  less)  to  large  spots  several  minutes 
of  arc  in  extent. 


THE  SUN. 


207 


Solar  spots  generally  have  a  dark  central  nucleus  or  umbra,  sur- 
rounded by  a  border  or  penumbra  of  grayish  tint,  intermediate  in 
shade  between  the  central  blackness  and  the  bright  photosphere. 
By  increasing  the  power  of  the  telescope,  the  spots  are  seen  to  be  of 
very  complex  forms.  The  umbra  is  often  extremely  irregular  in 
shape,  and  is  sometimes  crossed  by  bridges  or  ligaments  of  shining 
matter.  The  penumbra  is  composed  of  filaments  of  brighter  and 
darker  light,  which  are  arranged  in  striae.  The  general  aspect  of  a 
spot  under  considerable  magnifying  power  is  shown  in  Fig.  59. 

The  first  printed  account  of  solar  spots  was  given  by  FABRITIUS  in 
1611,  and  GALILEO  in  the  same  year  (May,  1611)  also  described  them. 


FIG.  59. — UMBRA  AND  PENUMBRA  OF  SUN-SPOT. 

GALILEO'S  observations  showed  them  to  belong  to  the  sun  itself,  and 
to  move  uniformly  across  the  solar  disk  from  east  to  west.  A  spot 
just  visible  at  the  east  limb  of  the  sun  on  any  one  day  travelled  slow- 
ly across  the  disk  for  12  or  14  days,  when  it  reached  the  west  limb, 
behind  which  it  disappeared.  After  about  the  same  period,  it  reap- 
pears at  the  eastern  limb,  unless,  as  is  often  the  case,  it  has  in  the 
mean  time  vanished. 

The  spots  are  not  permanent  in  their  nature,  but  are  formed  some- 
where on  the  sun,  and  disappear  after  lasting  a  few  days,  weeks,  or 
months.  But  so  long  as  they  last  they  move  regularly  from  east  to 
west  on  the  sun's  apparent  disk,  making  one  complete  rotation  iu 


208  ASTRONOMY. 

about  25  days.    This  period  of  25  days  is  therefore  approximately 
the  rotation  period  of  the  sun  itself. 

Spotted  Region. — It  is  found  that  the  spots  are  chiefly  confined  to 
two  zones,  one  in  each  hemisphere,  extending  from  about  10°  to  35 
or  40°  of  heliographic  latitude.  In  the  polar  region  spots  are 
scarcely  ever  seen,  and  on  the  solar  equator  they  are  much  more  rare 
than  in  latitudes  10°  north  or  south.  Connected  with  the  spots,  but 
lying  on  or  above  the  solar  surface,  are  fticufa,  moltlings  of  light 
brighter  lhan  the  general  surface  of  the  sun. 


Fio.  60.— PHOTOGRAPH  OF  THE  Rrx. 

Solar  Axis  and  Equator.  — The  spots  must  revolve  with  the  surface 
of  the  sun  about  his  axis,  and  the  directions  of  their  motions  must  be 
approximately  parallel  to  his  equator.  Fig.  61  shows  the  appear- 
ances as  actually  observed,  the  dotted  lines  representing  the  apparent 
paths  of  the  spots  across  the  sun's  disk  at  different  times  of  the  year. 
In  June  and  December  these  paths,  to  an  observer  on  the  earth,  seem 
to  be  right  lines,  and  hence  at  these  times  the  observer  must  be  in  the 
plane  of  the  solar  equator.  At  other  times  the  paths  are  ellipses,  and 
in  March  and  September  the  planes  of  these  ellipses  are  most  oblique, 
showing  the  spectator  to  be  then  furthest  from  the  plane  of  the  solar 
equator.  The  inclination  of  the  solar  equator  to  the  ecliptic  is  about 
7°  9',  and  the  axis  of  rotation  is  of  course  perpendicular  to  it. 


THE  SUN. 


209 


Nature  of  the  Spots. — The  sun-spots  are  really  depres 
sions  in  the  photosphere,  as  was  first  pointed  out  by  Atf- 
DREW  WILSON  of  Glasgow  in  1 774.  When  a  spot  is  seen  at 
the  edge  of  the  disk,  it  appears  as  a  notch  in  the  limb,  and  is 


FIG.  61.— APPARENT  PATH  OF  SOLAR  SPOT  AT  DIFFERENT  SEASONS. 

elliptical  in  shape.  As  the  rotation  carries  it  further  and 
further  on  to  the  disk,  it  becomes  more  and  more  nearly 
circula-r  in  shape,  and  after  passing  the  centre  of  the  disk 
the  appearances  take  place  in  reverse  order. 

These  observations  were  explained  by  WILSON,  and  more  fully  by 
Sir  WILLIAM  HE$SCHEL,  by  supposing  the  sun  to  consist  of  an  in. 


210 


ASTRONOMY. 


terior  dark  cool  mass,  surrounded  by  two  layers  of  clouds.  The 
outer  layer,  which  forms  the  visible  photosphere,  was  supposed  ex- 
tremely brilliaut.  The  iuuer  layer,  which  could  not  be  seen  except 
when  a  cavity  existed  in  the  photosphere,  was  supposed  to  be  dark. 
The  appearance  of  the  edges  of  a  spot,  which  has  been  described  as 
the  penumbra,  was  supposed  to  arise  from  those  dark  clouds.  The 
spots  themselves  are,  according  to  this  view,  nothing  but  openings 
through  both  of  the  atmospheres,  the  nucleus  of  the  spot  being  simply 
the  black  surface  of  the  inner  sphere  of  the  sun  itself. 
This  theory,  Fig.  62,  accounts  for  the  facts  as  they  were  known 


FIG.  62.— APPEARANCE  OF  A  SPOT  NKAR  THE  LIMB  AND  NEAR  THE 
CENTRE  OF  THE  SUN. 

to  HERSCHEL.  But  when  it  is  confronted  with  the  questions  of  the 
cause  of  the  sun's  heat  and  of  the  method  by  which  this  heat  has 
been  maintained  constant  in  amount  for  centuries,  it  breaks  down 
completely.  The  conclusions  of  WILSON  and  HERSCHEL,  that  the 
spots  are  depressions  in  the  sun's  surface,  are  undoubted.  But  the 
existence  of  a  cool  central  and  solid  nucleus  to  the  sun  is  now 
known  to  be  impossible.  The  apparently  black  centres  of  the  spots 
are  so  mostl3r  by  contrast.  If  they  were  seen  against  a  perfectly 
black  background,  they  would  appear  very  bright,  as  has  been 
proved  by  photometric  measures.  And  a  cool  solid  nucleus  beneath 


TEE  SUN. 

VC*5f    •  . 

.*f 

Bucli  an  atmosphere  as  HERSCHEL  supposed  would  soon  become  gas- 
eous by  the  conduction  and  radiation  of  the  heat  of  the  photosphere. 
The  supply  of  solar  heat,  which  has  been  very  nearly  constant  dur- 
ing the  historic  period,  in  a  sun  so  constituted  would  have  sensibly 
diminished  in  a  few  hundred  years.  For  these  and  other  reasons 
the  hypothesis  of  HEHSCHEL  must  be  modified,  save  as  to  the  fact 
that  the  spots  are  really  cavities  in  the  photosphere. 

Number  and  Periodicity  of  Solar  Spots. — The  number  of 
solar  spots  which  come  into  view  varies  from  year  to  year. 
Although  at  first  sight  this  might  seem  to  be  what  we  call 
a  purely  accidental  circumstance,  like  the  occurrence  of 
cloudy  and  clear  years  on  the  earth,  observations  of  sun- 
spots  establish  the  fact  that  this  number  varies  periodically. 

The  periodicity  of  the  spots  will  appear  from  the  following  sum- 
mary: 

From  1828  to  1831  the  sun  was  without  spots  on  only      1  day. 

In  1833  "  "  "  139  days. 

From  1836  to  1840  "  "  "                    3    " 

In  1843  "  "  "  147    " 

From  1847  to  1851  "  "  "                     2    " 

In  1856  "  "  "  193    " 

From  If 58  to  1861  "  "  "                   no    day. 

In  1867  "  "  "  195  days. 

Every  11  years  there  is  a  minimum  number  of  spots,  and  about  5 
years  after  each  minimum  there  is  a  maximum.  If,  instead  of  mere- 
ly counting  the  number  of  spots,  measurements  arc  made  on  solar 
photographs  of  the  extent  of  spotted  area,  the  period  comes  out  with 
greater  distinctness.  This  periodicity  of  the  area  of  the  solar  spots 
appears  to  be  connected  with  magnetic  phenomena  on  the  earth's 
surface,  and  with  the  number  of  auroras  visible.  It  has  been  sup- 
posed to  be  connected  also  with  variations  of  temperature,  of  rain- 
fall, and  with  other  meteorological  phenomena  such  as  the  monsoons 
of  the  Indian  Ocean,  etc.  The  cause  of  this  periodicity  is  as  yet  un- 
known. It  probably  lies  within  the  sun  itself,  and  is  similar  to  the 
cause  of  the  periodic  action  of  a  geyser.  As  the  periodic  variations 
of  the  spots  correspond  to  variations  of  the  magnetic  needle  on  the 
earth,  it  appears  that  there  is  a  connection  of  an  unknown  nature 
between  the  sun  and  the  earth.. 


212  ASTRONOMY. 


THE  SUN'S  CHROMOSPHERE  AND  CORONA. 

Phenomena  of  Total  Eclipses. — The  beginning  of  a  total  solar 
eclipse  is  marked  simply  by  the  small  black  notch  made  in  the 
luminous  disk  of  the  sun  by  the  advancing  edge  or  limb  of  the 
moon.  This  always  occurs  on  the  western  half  of  the  sun,  as  the 
moon  moves  from  west  to  east  in  ils  orbit.  An  hour  or  more  must 
elapse  before  the  moon  has  advanced  sufficiently  far  in  its  orbit  to 
cover  the  sun's  disk.  During  this  time  the  disk  of  the  sun  is  gradu- 
ally hidden  until  it  becomes  a  thin  crescent. 

The  actual  amount  of  the  sun's  light  may  be  diminished  to  two 
thirds  or  three  fourths  of  its  ordinary  amount  without  its  being 
strikingly  perceptible  to  the  eye.  What  is  first  noticed  is  the  change 
which  takes  place  in  the  color  of  the  surrounding  landscape,  which 
begins  to  wear  a  ruddy  aspect.  This  grows  more  and  more  pro- 
nounced,  and  gives  to  the  adjacent  country  that  weird  effect  which 
lends  so  much  to  the  impress! vcness  of  a  total  eclipse.  The  reason 
for  the  change  of  color  is  simple.  We  have  already  said  that  the 
sun's  atmosphere  absorbs  a  large  proportion  of  the  bluer  rays,  nnd  as 
this  absorption  is  dependent  on  the  thickness  of  the  solar  atmosphere 
through  which  the  rays  must  pass,  it  is  plain  that  just  before  the  sun 
is  totally  covered  the  rays  by  which  we  see  it  will  be  redder  than 
ordinary  sunlight,  as  they  are  those  which  come  from  points  near 
the  sun's  limb,  where  they  have  to  pass  through  the  greatest  thick- 
ness of  the  sun's  atmosphere. 

The  color  of  the  light  becomes  more  and  more  lurid  up  to  the  mo- 
ment when  the  sun  has  nearly  disappeared.  If  the  spectator  is  upon 
the  top  of  a  high  mountain,  he  can  then  begin  to  see  the  moon's 
shadow  rushing  toward  him  at  the  rate  of  a  kilometre  in  about  a 
second.  Just  as  the  shadow  reaches  him  there  is  a  sudden  increase 
of  darkness;  the  brighter  stars  begin  to  shine  in  the  dark  lurid  sky, 
the  thin  crescent  of  the  sun  breaks  up  into  small  points  or  dots  of 
light,  which  suddenly  disappear,  and  the  moon  itself,  an  intensely 
black  ball,  appears  to  hang  isolated  in  the  heavens. 

An  instant  afterward  the  corona  is  seen  surrounding  the  black 
disk  of  the  moon  with  a  soft  effulgence  quite  different  from  any 
other  light  known  to  us.  Near  the  moon's  limb  it  is  intensely  bright, 
and  to  the  naked  eye  uniform  in  structure;  5'  or  KX  from  the  limb 
this  inner  corona  has  a  boundary  more  or  less  defined,  and  from  this 
extend  streamers  and  wings  of  fainter  and  more  nebulous  light. 
These  are  of  various  shapes,  sizes,  and  brilliancy.  No  two  solar 
eclipses  yet  observed  have  been  alike  in  this  respect. 


THE  SUN.  213 

These  appearances,  though  changeable,  do  not  change  in  the  time 
the  moon's  shadow  requires  to  pass  from  Vancouver's  Island  to 
Texas,  for  example,  which  is  some  fifty  minutes. 

Superposed  upon  these  wings  may  be  seen  (sometimes  with  the 
naked  eye)  the  red  flames  or  protuberances  which  were  first  discov- 
ered during  a  solar  eclipse.  These  need  not  be  more  closely  de- 
scribed here,  as  they  can  now  be  studied  at  any  time  by  aid  of  the 
spectroscope. 

The  total  phase  lasts  for  a  few  minutes  (never  more  than  six  or 
seven),  and  during  this  time,  as  the  eye  becomes  more  and  more 
accustomed  to  the  faint  light,  the  outer  corona  is  seen  to  stretch 
further  and  further  away  from  the  sun's  limb.  At  the  eclipse  of  1878, 
July  29th,  it  was  seen  to  extend  more  than  6°  (about  9,000,000  miles) 
from  the  sun's  limb.  Just  before  the  end  of  the  total  phase  there  is 
a  sudden  increase  of  the  brightness  of  the  sky,  due  to  the  increased 
illumination  of  the  earth's  atmosphere  near  the  observer,  and  in  a 
moment  more  the  sun's  rays  are  again  visible,  seemingly  as  bright  as 
ever.  From  the  end  of  totality  till  the  last  contact  the  phenomena 
of  the  first  half  of  the  eclipse  are  repeated  in  inverse  order. 

Telescopic  Aspect  of  the  Corona, — Such  are  the  appearances  to  the 
naked  eye.  The  corona,  as  seen  through  a  telescope,  is,  however, 
of  a  very  complicated  structure.  The  inner  corona  is  usually  com- 
posed of  bright  striae  or  filaments  separated  by  darker  bands,  and 
some  of  these  latter  are  sometimes  seen  to  be  almost  totally  black. 
The  appearances  are  extremely  irregular,  but  they  are  often  as  if  the 
inner  corona  were  made  up  of  brushes  of  light  on  a  darker  back- 
ground. 

The  corona  and  red  prominences  are  solar  appendages.  It  was 
formerly  doubtful  whether  the  corona  was  an  atmosphere  belonging 
to  the  sun  or  to  the  moon.  At  the  eclipse  of  1860  it  was  proved  by 
measurements  that  the  red  prominences  belonged  to  the  sun  and  not 
to  the  moon,  since  the  moon  gradually  covered  them  by  its  motion, 
they  remaining  attached  to  the  sun.  The  corona  has  also  since  been 
shown  to  be  a  solar  appendage. 

Gaseous  Nature  of  the  Prominences. — The  eclipse  of  1868  (July) 
was  total  in  India,  and  was  observed  by  many  skilled  astronomers. 
A  discovery  of  M.  JANSSEN'S  will  make  this  eclipse  forever  memora- 
ble. He  was  provided  with  a  spectroscope,  and  by  it  observed  the 
prominences.  One  prominence  in  particular  was  of  vast  size,  and 
when  the  spectroscope  was  turned  upon  it,  its  spectrum  was  discon- 
tinuous, showing  the  bright  lines  of  hydrogen  gas. 

The  brightness  of  the  spectrum  was  so  marked  that  JANSSEN  deter- 
mined to  keep  his  spectroscope  fixed  upon  it  even  after  the  reappear- 


214 


ASTRONOMY. 


Fid.  63.— SUN'S  CORONA  DURING  THK  ECLIPSE  OF  JULY  29,  1878. 


THE  SUN. 


ance  of  sunlight,  to  see  how  long  it  could  be  followed.  It  was  found 
that  its  spectrum  could  still  be  seen  after  the  return  of  complete  sun- 
light; and  not  only  on  that  day,  but  on  subsequent  days,  similar 
phenomena  could  be  observed. 

One  great  difficulty  was  conquered  in  an  instant.  The  red  flames 
which  formerly  were  only  to  be  seen  for  a  few  moments  during  the 
comparatively  rare  occurrences  of  total  eclipses,  and  whose  observa- 
tion demanded  long  and  expensive  journeys  to  distant  parts  of  the 
world,  could  now  be  regularly  observed  with  all  the  facilities  offered 
by  a  fixed  observatory. 

This  great  step  in  advance  was  independently  made  by  Mr.  LOCK- 


Fia.  64.— FORMS  OF  THE  SOLAR  PROMINENCES  AS  SEEN  WITH  THE  SPECTROSCOPE. 

YER,  and  his  discovery  was  derived  from  pure  theory,  unaided  by  the 
eclipse  itself.  By  this  method  the  prominences  have  been  carefully 
mapped  day  by  day  all  around  the  sun,  and  it  has  been  proved  that 
around  this  body  there  is  a  vast  atmosphere  of  hydrogen  gas — the 
chromosphere  or  sierra.  From  out  of  this  the  prominences  are  pro- 
jected sometimes  to  heights  of  100,000  kilometres  or  more. 

It  will  be  necessary  to  recall  the  main  facts  of  observation  which 
are  fundamental  in  the  use  of  the  spectroscope.  When  a  brilliant 
point  is  examined  with  the  spectroscope,  it  is  spread  out  by  the  prism 
into  a  band — the  spectrum.  Using  two  prisms,  the  spectrum  be- 
comes longer,  but  the  light  of  the  surface,  being  spread  over  a 


216  ASTRONOMY. 

greater  area,  is  enfeebled.  Three,  four,  or  more  prisms  spread  out 
the  spectrum  proportionally  more.  If  the  spectrum  is  of  an  incan- 
descent solid  or  liquid,  it  is  always  continuous,  and  it  can  be  en- 
feebled to  any  degree ;  so  that  any  part  of  it  cau  be  made  as  feeble  as 
desired. 

This  method  is  precisely  similar  in  principle  to  the  use  of  the  tele- 
scope in  viewing  stars  in  the  daytime.  The  telescope  lessens  the 
brilliancy  of  the  sky,  while  the  disk  of  the  star  is  kept  of  the  same 
intensity,  as  it  is  a  point  in  itself.  It  thus  becomes  visible.  The 
spectrum  of  a  glowing  gas  will  consist  of  a  definite  number  of  lines, 
say  three — A,  B,  C,  for  example.  Now  suppose  the  spectrum  of  this 
gas  to  be  superposed  on  the  continuous  spectrum  of  the  sun;  by 
using  only  one  prism,  the  solar  spectrum  is  short  and  brilliant,  and 
every  part  of  it  may  be  more  brilliant  than  the  line  spectrum  of  the  gas. 
By  increasing  the  dispersion  (the  number  of  prisms),  the  solar  spec- 
trum is  proportionately  enfeebled.  If  the  ratio  of  the  light  of  the 
bodic-  ihrmxrlves.  the  sun  and  the  gas,  is  not  too  great,  the  continu- 
ous spectrum  may  be  so  enfeebled  that  the  line  spectrum  will  be 
visible  when  superposed  upon  it,  and  the  spectrum  of  the  gas  may 
then  be  seen  even  in  the  presence  of  true  sunlight.  Such  was  the 
process  imagined  and  successfully  carried  out  by  Mr.  LOCKYER,  and 
such  is  in  essence  the  method  of  viewing  the  prominences  to-day 
adopted. 

The  Coronal  Spectrum. — In  1869  (August  7th)  a  total  solar  eclipse 
was  visible  in  the  United  States.  It  was  probably  observed  by  more 
astronomers  than  any  preceding  eclipse.  Two  American  astron- 
omers, Professor  YOUNG,  of  Dartmouth  College,  and  Professor  HARK- 
NE88,  of  the  Naval  Observatory,  especially  observed  the  spectrum  of 
the  corona.  This  spectrum  was  found  to  consist  of  one  faint  green- 
ish line  crossing  a  faint  continuous  spectrum.  The  place  of  this  line 
in  the  maps  of  the  solar  spectrum  published  by  KIRCHHOFF  was  oc- 
cupied by  a  line  which  he  had  attributed  to  the  iron  spectrum,  and 
which  had  been  numbered  1474  in  his  list,  so  that  it  is  now  spoken 
of  as  1474  K.  This  line  is  probably  due  to  some  gas  which  must  be 
present  in  large  and  possibly  variable  quantities  in  the  corona,  and 
which  is  not  known  to  us  on  the  earth,  in  this  form  at  least.  It  is 
probably  a  gas  even  lighter  than  hydrogen,  as  the  existence  of  this 
line  has  been  traced  KX  or  30'  from  the  sun's  limb  nearly  all  around 
the  disk. 

In  the  eclipse  of  July  29th,  1878,  which  was  total  in  Colorado  and 
Texas,  the  continuous  spectrum  of  the  corona  was  found  to  be 
crossed  by  the  dark  lines  of  the  solar  spectrum,  showing  that  the 
coronal  light  was  composed  in  part  of  reflected  sunlight. 


TRE  StTtf.  217 

SOURCES  OF  THE  SUN'S  HEAT. 

Theories  of  the  Sun's  Constitution. — No  considerable 
fraction  of  the  heat  radiated  from  the  sun  returns  to  it 
from  the  celestial  spaces.  But  we  know  the  sun  is  daily 
radiating  into  space  2,170,000,000  times  as  much  heat  as 
is  daily  received  by  the  earth,  and  it  follows  that  unless 
the  supply  of  heat  is  infinite  (which  we  cannot  believe)  this 
enormous  daily  radiation  must  in  time  exhaust  the  supply. 
When  the  supply  is  exhausted,,  or  even  seriously  trenched 
upon,  the  result  to  the  inhabitants  of  the  earth  will  be  fatal. 
A  slow  diminution  of  the  daily  supply  of  heat  would  pro- 
duce a  slow  change  of  climates  from  hotter  toward  colder. 
The  serious  results  of  a  fall  of  50°  in  the  mean  annual  tem- 
perature of  the  earth  will  be  evident  when  we  remember 
that  such  a  fall  would  change  the  climate  of  France  to  that 
of  Spitzbergen.  The  temperature  of  the  sun  cannot  be 
kept  up  by  the  mere  combustion  of  its  materials.  If  the 
sun  were  solid  carbon,  and  if  a  constant  and  adequate  supply 
of  oxygen  were  also  present,  it  has  been  shown  that,  at  the 
present  rate  of  radiation,  the  heat  arising  from  the  com- 
bustion of  the  mass  would  not  last  more  than  6000  years. 

An  explanation  of  the  solar  heat  and  light  has  been  suggested, 
which  depends  upon  the  fact  that  great  amounts  of  heat  and  light 
are  produced  by  the  collision  of  two  rapidly  moving  heavy  bodies, 
or  even  by  the  passage  of  a  heavy  body  like  a  meteorite  through  the 
earth's  atmosphere.  In  fact,  if  we  had  a  certain  mass  available  with 
which  to  produce  heat  in  the  sun,  and  if  this  mass  were  of  the  best 
possible  materials  to  produce  heat  by  burning,  it  can  be  shown  that, 
by  burning  it  at  the  surface  of  the  sun,  we  should  produce  vastly 
less  heat  than  if  we  simply  allowed  it  to  fall  into  the  sun.  In  the 
last  case,  if  it  fell  from  the  earth's  distance,  it  would  give  6000  times 
more  heat  by  its  fall  than  by  its  burning. 

The  least  velocity  with  which  a  body  from  space  could  fall  upon 
the  sun's  surface  is  in  the  neighborhood  of  280  miles  in  a  second  of 


ASTRONOMY. 


time,  and  the  velocity  may  be  as  great  as  350  miles.  The  meteoric 
theory  of  solar  heat  is  in  effect  that  the  heat  of  the  sun  is  kept  up  by 
the  impact  of  meteors  upon  its  surface. 

No  doubt  immense  numbers  of  meteorites  fall  into  the  sun  daily 
and  hourly,  and  to  each  one  of  them  a  certain  considerable  portion 
of  heat  is  due.  It  is  found  that,  to  account  for  the  present  amount  of 
radiation,  meteorites  equal  in  mass  to  the  whole  earth  would  have  to 
fall  into  the  sun  every  century.  It  is  extremely  improbable  that  a 
mass  one  tenth  as  large  as  this  is  added  to  the  sun  in  this  way  per 
century,  if  for  no  other  reason  because  the  earth  itself  and  every 
planet  would  receive  far  more  than  its  present  share  of  meteorites, 
and  would  become  quite  hot  from  this  cause  alone. 

There  is  still  another  way  of  accounting  for  the  sun's  constant 
supply  of  energy,  and  this  has  the  advantage  of  appealing  to  no  cause 
outside  of  the  sun  itself  in  the  explanation.  It  is  by  supposing  the 
heat,  light,  etc.,  to  be  generated  by  a  constant  and  gradual  contrac- 
tion of  the  dimensions  of  the  solar  sphere.  As  the  globe  cools  by 
radiation  into  space,  it  must  contract.  In  so  contracting  its  ultimate 
constituent  parts  are  drawn  nearer  together  by  their  mutual  attrac- 
tion, whereby  a  form  of  energy  is  developed  which  can  be  trans- 
formed into  heat,  ligh*.  electricity,  or  other  physical  forces. 

This  theory  is  in  complete  agreement  with  the  known  laws  of 
force.  It  also  admits  of  precise  comparison  with  facts,  since  the 
laws  of  heat  enable  us,  from  the  known  amount  of  heat  radiated,  to 
infer  the  exact  amount  of  contraction  in  inches  which  the  linear 
dimensions  of  the  sun  must  undergo  in  order  that  this  supply  of  heat 
may  be  kept  unchanged,  as  it  is  practically  found  to  be.  With  the 
present  size  of  the  sun,  it  is  found  that  it  is  only  necessary  t<>  sup- 
pose that  its  diameter  is  diminishing  at  the  rate  of  about  220  feet  per 
year,  or  4  miles  per  century,  in  order  that  the  supply  of  heat  radiated 
shall  be  constant.  It  is  plain  that  such  a  change  us  this  may  be 
taking  place,  since  we  possess  no  instruments  sufficiently  delicate  to 
have  detected  a  change  of  even  ten  times  this  amount  since  the  in- 
vention of  the  telescope. 

It  may  seem  a  paradoxical  conclusion  that  the  cooling  of  a  body 
may  cause  it  to  become  hotter.  This  indeed  is  true  only  when  we 
suppose  the  interior  to  be  gaseous,  and  not  solid  or  liquid.  It  is, 
however,  proved  by  theory  that  this  law  holds  for  gaseous  masses. 

We  cannot  say  whether  the  sun  has  yet  begun  to  liquefy 
in  his  interior  parts,  and  hence  it  is  impossible  to  predict 
at  present  the  duration  of  his  constant  radiation.  Theory 


THE  SVtf.  219 

shows  us  that  after  about  5,000,000  years,  the  sun  radiat- 
ing heat  as  at  present,  and  still  remaining  gaseous,  will  be 
reduced  to  one  half  of  his  present  volume.  It  seems  prob- 
able that  somewhere  about  this  time  the  solidification  will 
have  begun,  and  it  is  roughly  estimated,  from  this  line  of 
argument,  that  the  present  conditions  of  heat  radiation 
cannot  last  greatly  over  10,000,000  years. 

The  future  of  the  sun  (and  hence  of  the  earth)  cannot, 
as  we  see,  be  traced  with  great  exactitude.  The  past  can 
be  more  closely  followed  if  we  assume  (which  is  tolerably 
safe)  that  the  sun  up  to  the  present  has  been  a  gaseous  and 
not  a  solid  or  liquid  mass.  Four  hundred  years  ago,  then, 
the  sun  was  about  16  miles  greater  in  diameter  than  now; 
and  if  we  suppose  this  process  of  contraction  to  have  regu- 
larly gone  on  at  the  same  rate  (an  uncertain  supposition), 
we  can  fix  a  date  when  the  sun  filled  any  given  space,  out 
even  to  the  orbit  of  Neptune;  that  is,  to  the  time  when 
the  solar  system  consisted  of  but  one  body,  and  that  a  gas- 
eous or  nebulous  one.  It  will  subsequently  be  seen  that 
the  ideas  here  reached  a  posteriori  have  a  striking  analogy 
to  the  a  priori  ideas  of  KANT  and  LA  PLACE. 

It  is  not  to  be  taken  for  granted,  however,  that  the 
amount  of  heat  to  be  derived  from  the  contraction  of  the 
sun's  dimensions  is  infinite,  no  matter  how  large  the  prim- 
itive dimensions  may  have  been.  A  body  falling  from  any 
distance  to  the  sun  can  only  have  a  certain  finite  velocity 
depending  on  this  distance  and  the  mass  of  the  sun  itself, 
which,  even  if  the  fall  be  from  an  infinite  distance,  cannot 
exceed,  for  the  sun,  350  miles  per  second.  In  the  same 
way  the  amount  of  heat  generated  by  the  contraction  of  the 
sun's  volume  from  any  size  to  any  other  is  finite  and  not 
infinite. 


220  ASTRONOMY. 

It  has  been  shown  that  if  the  sun  has  always  been  radi- 
ating heat  at  its  present  rate,  and  if  it  had  originally  filled 
all  space,  it  has  required  18,000,000  years  to  contract  to  its 
present  volume.  In  other  words,  assuming  the  present 
rate  of  radiation,  and  taking  the  most  favorable  case,  the 
age  of  the  sun  does  not  exceed  18,000,000  years.  The 
earth  is,  of  course,  less  aged.  The  supposition  lying  at 
the  base  of  this  estimate  is  that  the  radiation  of  the  sun 
has  been  constant  throughout  the  whole  period.  This  is 
quite  unlikely,  and  any  changes  in  this  datum  affect  greatly 
the  final  number  of  years  which  we  have  assigned.  While 
this  number  may  be  greatly  in  error,  yet  the  method  of 
obtaining  it  seems,  in  the  present  state  of  science,  to  be 
satisfactory,  and  the  main  conclusion  remains  that  the  past 
of  the  sun  is  finite,  and  that  in  all  probability  its  future  is 
a  limited  one.  The  exact  number  of  centuries  that  it  is  to 
last  are  of  no  moment  even  were  the  data  at  hand  to  obtain 
them:  the  essential  point  is  that,  so  far  as  we  can  see,  the 
sun,  and  incidentally  the  solar  system,  has  a  finite  past  and 
a  limited  future,  and  that,  like  other  natural  objects,  it 
passes  through  its  regular  stages  of  birth,  vigor,  decay,  and 
death,  in  one  order  of  progress. 


CHAPTER  III. 
THE   INFERIOR  PLANETS. 


MOTIONS  AND  ASPECTS. 

THE  inferior  planets  are  those  whose  orbits  lie  between  the  sun 
and  the  orbit  of  the  earth.  Commencing  with  the  more  distant  ones, 
they  comprise  Venus  and  Mercury. 

The  real  and  apparent  motions  of  these  planets  have  already  been 
briefly  described  in  Part  I.,  Chapter  V.  It  will  be  remembered  that, 
in  accordance  with  KEPLER'S  third  law,  their  periods  of  revolution 
around  the  sun  are  less  than  that  of  the  earth.  Consequently  they 
overtake  the  latter  between  successive  inferior  conjunctions. 

The  interval  between  these 
conjunctions  is  about  four 
months  in  the  case  of  Mer- 
cury, and  between  nineteen 
and  twenty  months  in  that  of 
Venus.  At  the  end  of  this 
period  each  repeats  the  same 
series  of  motions  relative  to 
the  sun.  What  these  motions 
are  can  be  readily  seen  by 
studying  Fig.  65.  In  the  first 
place,  suppose  the  earth  at 
any  point,  E,  of  its  orbit,  and 
if  we  draw  a  line,  E  L  or 
EM,  from  E,  tangent  to  the 


PIG 


orbit  of  either  of  these  planets, 
it  is  evident   that  the  angle 

which  this  line  makes  with  that  drawn  to  the  sun  is  the  greatest 
elongation  of  the  planet  from  the  sun.  The  orbits  being  eccentric, 
this  elongation  varies  with  the  position  of  the  earth.  In  the  case 
of  Mercury  it  ranges  from  16°  to  29°,  while  in  the  case  of  Venus,  the 
orbit  of  which  is  nearly  circular,  it  varies  very  little  from  45°.  These 
planets,  therefore,  seem  to  have  an  oscillating  motion,  first  swinging 


ABTRONOMT. 


toward  the  east  of  the  sun,  and  then  toward  the  west  of  it,  as  already 
explained.  Since,  owing  to  the  annual  revolution  of  the  earth,  the 
sun  has  a  constant  eastward  motion  among  the  stars,  these  planets 
must  have,  on  the  whole,  a  corresponding  though  intermittent  motion 
in  the  same  direction.  Therefore  the  ancient  astronomers  supposed 
their  period  of  revolution  to  be  one  year,  the  same  as  that  of  the 
sun. 

If,  again,  we  draw  a  line  E  S  C  from  the  earth  through  the  sun,  the 
point  /,  in  which  this  line  cuts  the  orbit  of  the  planet,  or  the  point 
of  inferior  conjunction,  will  be  the  least  distance  of  the  planet  from 

the  earth,  while  the  second  point  C, 
or  the  point  of  superior  conjunction, 
on  the  opposite  side  of  the  sun,  will 
be  the  irreatc-t  di>laiirc.  Owing  to 
the  difference  of  ihe>e  distances  the 
apparent  magnitude,  of  these  planets, 
as  seen  from  the  earih,  is  subject  to 
Fio.  66.—  APPARENT  MAGNITUDES  great  variations. 

OF  THE   DIS*  OF   MEBCURT.  j,^     ,.,.   ^^   j,,^  variutionS  ill  tllO 

case  of  Mercury,  A  representing  its  apparent  magnitude  when  at  its 
greatest  distance,  B  when  at  its  mean  distance,  and  C  when  at  its 
least  distance.  In  the  case  of  Venus  (Fig.  C7)  the  variations  are  much 
greater  than  in  that  of  Mercury,  the  greatest  distance,  1.72,  being 
more  than  six  times  the  least  distance,  which  is  only  0.28.  The 
variations  of  apparent  magnitude  are  therefore  great  in  the  same 
proportion. 

In  thus  representing  the  apparent  angular  magnitude  of  these 
planets,  we  suppose  their  whole  disks  to  be  visible,  as  they  would  be 
if  they  shone  by  their  own  light.  But  since  they  can  be  seen  only  by 
the  reflected  light  of  the  sun,  only  those  portions  of  the  disk  can  be 
seen  which  are  at  the  same  time  visible  from  the  sun  and  from  the 
earth.  A  very  little  consideration  will  show  that  the  proportion  of 
the  disk  which  can  be  seen  constantly  diminishes  as  the  planet  ap- 
proaches the  earth,  and  looks  larger. 

When  the  planet  is  at  its  greatest  distance,  or  in  superior  conjunction 
(C,  Fig.  65),  its  whole  illuminated  hemisphere  can  be  seen  from  the 
earth.  As  it  moves  around  and  approaches  the  earth,  the  illuminated 
hemisphere  is  gradually  turned  from  us.  At  the  point  of  greatest 
elongation,  M  or  L,  one  half  the  hemisphere  is  visible,  and  the 
planet  has  the  form  of  the  moon  at  first  or  second  quarter.  As  it 
approaches  inferior  conjunction,  the  apparent  visible  disk  assumes 
the  form  of  a  crescent,  which  becomes  thinner  and  thinner  as  the 
planet  approaches  the  sun. 


THE  INFERIOR  PLANETS. 


223 


Fi?.  68  shows  the  apparent  disk  of  Mercury  at  various  times  during 
its  synodic  revolution.  The  planet  will  appear  brightest  when  this 
disk  has  the  greatest  surface.  This  occurs  about  half  way  between 
greatest  elongation  and  inferior  conjunction. 

In  consequence  of  the  changes  in  the  brilliancy  of  these  planets 
produced  by  the  variations  of  distance,  and  those  produced  by  the 


FIG.  67.— APPARENT  MAGNITUDES  OF  THE  DISK  OF  VENUS. 

variations  in  the  proportion  of  illuminated  disk  visible  from  the 
earth,  partially  compensating  each  other,  their  actual  brilliancy  is 
not  subject  to  such  great  variations  as  might  have  been  expected. 
As  a  general  rule,  Mercury  shines  with  a  light  exceeding  that  of  a 
star  of  the  first  magnitude.  But  owing  to  its  proximity  to  the  sun, 


A 


>  > 


«  <  cc 


FIG.  68.— APPEARANCE  OP  MERCURY  AT  DIFFERENT  POINTS  OF  ITS  ORBIT. 

it  can  never  be  seen  by  the  naked  eye  except  in  the  west  a  short  time 
after  sunset,  and  in  the  east  a  little  before  sunrise.  It  is  then  of 
necessity  near  the  horizon,  and  therefore  does  not  seem  so  bright  as 
if  it  were  at  a  greater  altitude.  In  our  latitudes  we  might  almost 
say  that  it  is  never  visible  except  in  the  morning  or  evening  twilight 


224  ASTRONOMY. 

On  the  other  hand,  the  planet  Venn*  is,  next  to  the  sun  and  moon, 
the  most  brilliant  object  in  the  heavens.  It  is  so  much  brighter 
than  any  fixed  star  that  there  can  seldom  be  any  difficulty  in  identi- 
fying it.  The  unpractised  observer  might  under  some  circumstances 
find  a  difficulty  in  distinguishing  between  Venus  and  Jupiter,  but 
the  different  motions  of  the  two  planets  will  enable  him  to  distin- 
guish them  if  they  are  watched  from  night  to  night  during  several 
weeks. 

ATMOSPHERE  AND  ROTATION  OF  MERCURY. 

The  various  phases  of  Mercury,  as  dependent  upon  its  various 
positions  relative  to  the  sun.  have  already  1>« «  n  shown.  If  the  planet 
were  an  opaque  sphere,  without  inequalities  and  without  an  atmos- 
phere, the  apparent  disk  would  always  be  bounded  by  a  circle  on 
one  side  and  an  ellipse  on  the  other,  as  represented  in  the  figure. 
Whether  any  variation  from  this  simple  and  perfect  form  has  ever 
been  detected  is  an  open  question,  the  balance  of  evidence  being  very 
strongly  in  the  negative.  Since  no  spots  are  visible  upon  it,  it  would 
follow  that  unless  variations  of  form  due  to  inequalities  on  its  sur- 
face, such  as  mountains,  can  be  detected,  it  is  impossible  to  deter- 
mine whether  the  planet  rotates  on  its  axis. 

We  may  regard  it  as  doubtful  whether  any  evidence  of  an  atmos- 
phere of  Mercury  has  been  obtained,  and  it  is  certain  that  we  know 
nothing  definite  respecting  its  physical  constitution. 

ATMOSPHERE  AND  ROTATION  OF  VENUS. 

As  Venus  sometimes  comes  nearer  the  earth  than  any  other  pri- 
mary planet,  astronomers  have  examined  its  surface  with  great  at- 
tention ever  since  the  invention  of  the  telescope.  But  no  conclusive 
evidence  respecting  the  rotation  of  the  planet  and  no  proof  of  any 
changes  or  any  inequalities  on  its  surface  have  ever  been  obtained. 

Atmosphere  of  Venus. — The  evidence  of  an  atmosphere  of  Venus  is 
perhaps  more  conclusive  than  in  the  case  of  any  other  planet. 
When  Venus  is  observed  very  near  its  inferior  conjunction,  and 
when  it  therefore  presents  the  view  of  a  very  thin  crescent,  it  is 
found  that  this  crescent  extends  over  more  than  180°.  This  would 
be  evidently  impossible  unless  the  sun  illuminated  more  than  one 
half  the  planet.  We  therefore  conclude  that  Venus  has  an  atmos- 
phere which  exercises  so  powerful  a  refraction  upon  the  light  of  the 
sun  that  the  latter  illuminates  several  degrees  more  than  one  half  the 
globe.  A  phenomenon  which  must  be  attributed  to  the  same  cause 
has  several  times  been  observed  during  transits  of  Venus.  During 


THE  INFERIOR  PLANETS.  225 

the  transit  of  December  8th,  1874,  most  of  the  observers  who  enjoyed 
a  fine  steady  atmosphere  saw  that  when  Venus  was  partially  pro- 
jected on  the  sun,  the  outline  of  that  part  of  its  disk  outside  the  sun 
could  be  distinguished  by  a  delicate  line  of  light.  From  these 
several  observations  it  would  seem  that  the  refractive  power  of  the 
atmosphere  of  Venus  is  greater  than  that  of  the  earth. 

TRANSITS  OF  MERCURY  AND  VENUS. 

When  Mercury  or  Venus  passes  between  the  earth  and  sun,  so  as 
to  appear  projected  on  the  sun's  disk,  the  phenomenon  is  called  a 
transit.  If  these  planets  moved  around  the  sun  in  the  plane  of  the 
ecliptic,  it  is  evident  that  there  would  be  a  transit  at  every  inferior 
conjunction. 

The  longitude  of  the  descending  node  of  Mercury  at  the  present 
time  is  227°,  and  therefore  that  of  the  ascending  node  47°.  The 
earth  has  these  longitudes  on  May  7th  and  November  9th.  Since  a 
transit  can  occur  only  within  a  few  degrees  of  a  node,  Mercury  can 
transit  only  within  a  few  days  of  these  epochs. 

The  longitude  of  the  descending  node  of  Venus  is  now  about  256* 
and  therefore  that  of  the  ascending  node  is  76°.    The  earth  has  these 
longitudes  on  June  6th  and  December  7th  of  each  year.     Transits  of 
Venus  can  therefore  occur  only  within  two  or  three  days  of  these 
times. 

Recurrence  of  Transits  of  Mercury. — The  following  table  shows  the 
dates  of  occurrence  of  transits  of  Mercury  during  the  present  cen- 
tury. They  are  separated  into  May  transits,  which  occur  near  the 
descending  node,  and  November  ones,  which  occur  near  the  ascend- 
ing node.  November  transits  are  the  most  numerous,  because 
Mercury  is  then  nearer  the  sun,  and  the  transit  limits  are  wider. 

1799,  May  6.  1802,  Nov.  9. 

1832,  May  5.  1815,  Nov.  11. 

1845,  May  8.  1822,  Nov.  5. 

1878,  May  6.  1835,  Nov.  7. 

1891,  May  9.  1848,  Nov.  10. 

1861,  Nov.  12. 

1868,  Nov.    5. 

1881,  Nov.    7. 

1894,  Nov.  10. 

Recurrence  of  Transits  of  Venus. — For  many  centuries  past  and  to 
come,  transits  of  Venus  occur  in  a  cycle  more  exact  tlian  those  of 


ASTRONOMY. 


Mercury.  It  happens  that  Venut  makes  13  revolutions  around  the 
sun  in  nearly  the  same  lime  that  the  earth  makes  8  revolutions;  that 
is,  in  eight  years.  During  this  period  tiiere  will  be  5  inferior  con- 
junctions  of  Venus,  because  the  latter  has  made  5  revolutions  more 
than  the  earth.  Consequently,  if  we  wait  eight  years  from  an  inferior 
conjunction  of  Venus,  we  shall,  at  the  end  of  that  time,  have  another 
inferior  conjunction,  the  fifth  in  regular  order,  at  nearly  the  same 
point  of  the  two  orbits.  It  will,  therefore,  occur  at  the  same  time 
of  the  year,  ami  in  nearly  the  same  position  relative  to  the  node  of 
Venus. 

After  a  pair  of  transits  8  years  apart,  an  interval  of  over  100  years 
must  elapse  before  the  occurrence  of  another  pair  as  is  shown  in  the 
following  table.  The  dates  and  intervals  of  the  transits  for  three 
cycles  nearest  to  the  present  time  are  as  follows: 


1518,  June  2. 

1761,  June  5. 

2004,  June  8 

Intervals. 
8  years. 

1526,  June  1. 

1769,  June  3. 

2012,  June  6. 

105*  •' 

1631,  Dec.  7. 

1874,  Dec.  9. 

2117,  Dec.  11. 

8   " 

163V,  Dec.  4. 

1882,  Dec.  6. 

2125,  Dec.  8 

121i  " 

SUPPOSED   INTEAMERCUEIAL  PLANETS. 

Some  astronomers  are  of  opinion  that  there  is  a  small  planet  or 
a  group  of  planets  revolving  around  the  sun  inside  the  orbit  of 
Mercury.  To  this  supposed  planet  the  name  Vulcan  has  been  given; 
but  astronomers  generally  discredit  the  existence  of  any  such  planet 
of  considerable  size. 

The  evidence  in  favor  of  the  existence  of  such  planets  may  be 
divided  into  three  classes,  as  follows,  which  will  be  considered  in 
their  order: 

(1)  A  motion  of  the  perihelion  of  the  orbit  of  Mercury,  supposed 
to  be  due  to  the  attraction  of  such  a  planet  or  group  of  plunets. 

(2)  Transits  of  dark  bodies  across  the  disk  of  the  sun  which  have 
been  supposed  to  be  seen  by  various  observers  during  the  past  cen- 
tury. 

(3)  The  observation  of  certain  unidentified  objects  by  Professor 
WATSON  and  Mr.  LEWIS  SWIFT  during  the  total  eclipse  of  the  sun, 
July  29th,  1878. 

(1)  In  1858  LE  VERRIER  made  a  careful  collection  of  all  the  obser- 
vations on  the  transits  of  Mercury  which  had  been  recorded  since  the 
invention  of  the  telescope.  The  result  of  that  investigation  was 


THE  INFERIOR  PLANETS.  227 

that  the  observed  times  of  transit  could  not  be  reconciled  with  the 
calculated  motion  of  the  planet,  as  due  to  the  gravitation  of  the 
other  bodies  of  the  solar  system.  He  found,  however,  that  if,  in 
addition  to  the  changes  of  the  orbit  due  to  the  attraction  of  the 
known  planets,  he  supposed  a  motion  of  the  perihelion  amounting  to 
36"  in  a  century,  the  observations  could  all  be  satisfied.  Such  a 
motion  might  be  produced  by  the  attraction  of  an  unknown  planet 
inside  the  orbit  of  Mercury.  Since,  however,  a  single  planet,  in 
order  to  produce  this  effect,  would  have  to  be  of  considerable  size, 
and  since  no  such  object  had  ever  been  observed  during  a  total 
eclipse  of  the  sun,  he  concluded  that  there  was  probably  a  group  of 
planets  much  too  small  to  be  separately  distinguished. 

(2)  It  is  to  be  noted  that  if  such  planets  existed  they  would  fre- 
quently pass  over  the  disk  of  the  sun.     During  the  past  fifty  years 
the  sun  has  been  observed   almost  every  day  with  the  greatest  $ 
assiduity  by  eminent  observers,  armed  with  powerful  instruments, 
who  have  made  the  study  of  the  sun's  surface  and  spots  the  principal 
work  of  their  lives.     None  of  these  observers  has  ever  recorded  the 
transit  of  an  unknown  planet.     This  evidence,  though  negative  in 
form,  is,  under  the  circumstances,  conclusive  against  the  existence 
of  such  a  planet  of  such  magnitude  as  to  be  visible  in  transit  with 
ordinary  instruments. 

(3)  The  observations  of  Professor  WATSON  during  the  total  eclipse 
above  mentioned  seem  to  afford  the  strongest  evidence  yet  obtained 
in  favor  of  the  real  existence  of  the  planet.    His  mode  of  proceeding 
was  briefly  this:  Sweeping  to  the  west  of  the  sun  during  the  eclipse, 
he  saw  two  objects  in  positions  where,  supposing  the  pointing  of  his 
telescope  accurately  known,  no  fixed  star  existed.     There  is,  how- 
ever, a  pair  of  known  stars,  one  of  which  is  about  a  degree  distant 
from  one  of  the  unknown  objects,  and  the  other  about  the  same 
distance  and  direction  from  the  second.    It  is  probable  that  Professor 
WATSON'S  supposed  planets  were  this  pair  of  stars. 

Since  the  above  was  written  Prof.  WATSON'S  observations  have 
been  repeated  under  exceptionally  favorable  circumstances  at  the 
eclipse  of  May  6,  1883,  and  no  trace  of  his  supposed  planets  was  seen, 
while  much  smaller  stars  were  observed. 


CHAPTER  IV. 

THE  MOON. 

WHEN  it  became  clearly  understood  that  the  earth  and 
moon  were  to  be  regarded  as  bodies  of  one  class,  and  that 
the  old  notion  of  an  impassable  gulf  between  the  character 
of  bodies  celestial  and  bodies  terrestrial  was  unfounded, 
the  question  whether  the  moon  was  like  the  earth  in  all  its 
details  became  one  of  great  interest.  The  point  of  most 
especial  interest  was  whether  the  moon  could,  like  the 
earth,  be  peopled  by  intelligent  inhabitants.  Accordingly, 
when  the  telescope  was  invented  by  GALILEO,  one  of  the 
first  objects  examined  was  the  moon.  With  every  im- 
provement of  the  instrument  the  examination  became 
more  thorough,  so  that  at  present  the  topography  of  the 
moon  is  much  better  known  than  that  of  the  State  of 
Arkansas,  for  example. 

With  every  improvement  in  the  means  of  research,  it 
has  become  more  and  more  evident  that  the  surface  of  the 
moon  is  totally  unlike  that  of  our  earth.  There  are  no 
oceans,  seas,  rivers,  air,  clouds,  or  vapor.  We  can  hardly 
suppose  that  animal  or  vegetable  life  exists  under  such  cir- 
cumstances, the  fundamental  conditions  of  such  existence 
on  our  earth  being  entirely  wanting.  We  might  almost  as 
well  suppose  a  piece  of  granite  or  lava  to  be  the  abode  of 
life  as  the  surface  of  the  moon. 

The  length  of  one  mile  on  the  moon  would.tas  seen  from 


THE  MOON.  229 

the  earth,  subtend  an  angle  of  about  Y  of  arc.  More 
exactly,  the  angle  subtended  would  range  between  Off.8  and 
0*.9,  according  to  the  varying  distance  of  the  moon.  In 
order  that  an  object  may  be  plainly  visible  to  the  naked 
eye,  it  must  subtend  an  angle  of  nearly  1'.  Consequently 
a  magnifying  power  of  60  is  required  to  render  a  round 
object  one  mile  in  diameter  on  the  surface  of  the  moon 
plainly  visible.  Starting  from  this  fact,  we  may  readily 
form  the  following  table,  showing  the  diameters  of  the 
smallest  objects  that  can  be  seen  with  different  magnifying 
powers,  always  assuming  that  vision  with  these  powers  is 
perfect: 

Power      60;  diameter  of  object  1  mile. 
Power    150;  diameter  2000  feet. 
Power    500;  diameter  600  feet. 
Power  1000;  diameter  300  feet. 
Power  2000;  diameter  150  feet. 

If  telescopic  power  could  be  increased  indefinitely,  there 
would  of  course  be  no  limit  to  the  minuteness  of  an  object 
visible  on  the  moon's  surface.  But  the  necessary  imper- 
fections of  all  telescopes  are  such  that  only  in  extraordinary 
cases  can  anything  be  gained  by  increasing  the  magnifying 
power  beyond  1000.  The  influence  of  warm  and  cold  cur- 
rents in  our  atmosphere  will  forever  prevent  the  advan- 
tageous use  of  high  magnifying  powers.  After  a  certain 
limit  we  see  nothing  more  by  increasing  the  power,  vision 
becoming  indistinct  in  proportion  as  the  power  is  increased. 
It  is  hardly  likely  that  an  object  less  than  600  feet  in  extent 
can  ever  be  seen  on  the  moon  by  any  telescope  whatever, 
unless  it  becomes  possible  to  mount  the  instrument  above 
the  atmosphere  of  the  earth.  It  is  therefore  only  the  great 
features  on  the  surface  of  the  moon,  and  not  the  minute 
ones,  which  can  be  made  out  with  the  telescope. 


230 


ASTRONOMY. 


FIG.  69.— ASPECT  OF  THB  MOON'S  SURFACE. 

Character  of  the  Moon's  Surface.— The  most  striking  point  of 
ference  between  the  earth  and  moon  is  seen  in  the  total  absence  * 
the  latter  of  anything  that  looks  like  an  undulating  surface. 


MOON. 


formations  similar  to  our  valleys  and  mountain-chains  have  been 
detected.  The  lowest  surface  of  the  moon  which  can  be  seen  with 
the  telescope  appears  to  be  nearly  smooth  and  flat,  or,  to  speak 
more  exactly,  spherical  (because  the  moon  is  a  sphere).  This  sur- 
face has  different  shades  of  color  in  different  regions.  Some  por- 
tions are  of  a  bright  silvery  tint,  while  others  have  a  dark  gray  ap- 
pearance. These  differences  of  tint  seem  to  arise  from  differences  of 
material. 

Upon  this  surface  as  a  foundation  are  built  numerous  formations 
of  various  sizes,  but  all  of  a  very  simple  character.  Their  general 
form  can  be  made  out  by  the  aid  of  Fig.  69,  and  their  dimensions  by 
the  scale  of  miles  at  the  bottom  of  it.  The  largest  and  most  promi- 
nent features  are  known  as  craters.  They  have  a  typical  form  con- 
sisting of  a  round  or  oval  rugged  wall  rising  from  the  plane  in  the 
manner  of  a  circular  fortification.  These  walls  are  frequently  from 
three  to  six  thousand  metres  in  height,  very  rough  and  broken.  In 
their  interior  we  see  the  plane  surface  of  the  moon  already  described. 
It  is,  however,  generally  covered  with  fragments  or  broken  up  by 
small  'inequalities  so  as  not  to  be  easily  made  out.  In  the  centre  of 
the  craters  we  frequently  find  a  conical  formation  rising  up  to  a  con- 
siderable height,  and  much  larger  than  the  inequalities  just  described. 
In  the  craters  we  have  a  vague  resemblance  to  volcanic  formations 
upon  the  earth,  the  principal  difference  being  that  their  magnitude  is 
very  much  greater  than  anything  known  here.  The  diameter  of  the 
larger  ones  ranges  from  50  to  200  kilometres,  while  the  smallest  are 
so  minute  as  to  be  hardly  visible  with  the  telescope. 

When  the  moon  is  only  a  few  days  old,  the  sun's  rays  strike  very 
obliquely  upon  the  lunar  mountains,  and  they  cast  long  shadows. 
'from  the  known  position  of  the  sun,  moon,  and  earth,  and  from  the 
measured  length  of  these  shadows,  the  heights  of  the  mountains  can 
be  calculated.  It  is  thus  found  that  some  of  the  mountains  near  the 
south  pole  rise  to  a  height  of  8000  or  9000  metres  (from  25,000  or  30,000 
.  feet)  above  the  general  surface  of  the  moon.  Heights  of  from  3000 
to  7000  metres  are  very  common  over  almost  the  whole  lunar  surface. 
;  The  question  of  the  origin  of  the  lunar  features  has  a  bearing  on 
theories  of  terrestrial  geology  as  well  as  upon  various  questions  re- 
specting the  past  history  of  the  moon  itself.  It  has  been  considered 
'"\  this  aspect  by  various  geologists. 

"unar  Atmosphere.  —  The  question  whether  the  moon  has  an  atmos- 
are  has  been  much  discussed.  The  only  conclusion  which  has  yet 
•n  reached  is  that  no  positive  evidence  of  an  atmosphere  has  ever 

an  obtained,  and  that  if  one  exists  it  is  certainly  several  hundred 
A)S  rarer  than  the  atmosphere  of  our  earth. 


232  ASTRONOMY. 

Light  and  Heat  of  the  Moon.— Many  attempts  have  been  made  to 
measure  the  ratio  of  the  light  of  the  full  moon  and  that  of  the  sun. 
The  results  have  been  very  discordant,  but  all  have  agreed  in  show- 
ing that  the  sun  emits  several  hundred  thousand  times  as  much  light 
as  the  full  moon.  The  last  and  most  careful  determination  is  that  of 
ZOLLNER,  who  finds  the  sun  to  be  618,000  times  as  bright  as  the  full 
moon. 

The  moon  must  reflect  the  heat  as  well  as  the  light  of  the  sun,  and 
must  also  radiate  a  small  amount  of  its  own  heat.  The  latest  re- 
searches indicate  that  the  amount  received  by  the  earth  is  inappre- 
ciable. 

Is  there  any  Change  on  the  Surface  of  the  Moon  t — When  the  sur- 
face of  the  moon  was  first  found  to  be  covered  by  craters  having  the 
appearance  of  volcanoes  at  the  surface  of  the  earth,  it  was  very 
naturally  thought  that  these  supposed  volcanoes  might  be  still  in 
activity,  and  exhibit  themselves  to  our  telescopes  by  I  heir  flamei. 
Not  the  slightest  sound  evidence  of  any  incandescent  eruption  at  the 
moon's  surface  has  been  found,  however. 

Several  instances  of  supposed  changes  of  shape  of  features  on  the 
moon's  surface  have  been  described  in  recent  times. 

The  question  whether  these  changes  are  proven  is  one  on  which 
the  opinions  of  astronomers  differ.  The  difficulty  of  reaching  a  cer- 
tain conclusion  arises  from  the  fact  that  each  feature  necessarily 
varies  in  appearance,  owing  to  the  different  directions  in  which  the 
sun's  light  falls  upon  it.  Sometimes  the  changes  arc  very  difficult 
to  account  for,  even  when  it  is  certain  that  they  do  not  arise  from 
any  change  on  the  moon  itself.  Hence  while  some  regard  the  appa- 
rent changes  as  real,  others  regard  them  as  due  only  to  differences  in 
the  mode  of  illumination. 

The  Moon  only  Shows  one  Face  to  the  Earth.— The  moon  rotates  on 
her  axis  from  west  to  east,  and  the  time  required  for  one  rotation  is 
the  same  as  that  required  for  one  revolution  in  her  orbit.  If  a  line 
be  drawn  from  the  earth  to  the  moon,  this  line  will  always  touch  the 
same  hemisphere  of  the  moon :  and  the  moon  does  not  rotate  at  all 
with  reference  to  this  line.  But  if  any  line  be  drawn  through  the 
sun  parallel  to  the  moon's  axis,  the  moon  sometimes  turns  one  face 
and  sometimes  another  to  this  line.  An  observer  on  the  earth,  how- 
ever, sees  but  one  hemisphere  of  the  moon. 


CHAPTER  V. 
THE  PLANET  MARS. 

DESCRIPTION  OF  THE  PLANET. 

Mars  is  the  next  planet  beyond  the  earth  in  the  order  of 
distance  from  the  sun,  being  about  half  as  far  again  as  the 
earth.  It  has  a  decided  red  color,  by  which  it  may  be 
readily  distinguished  from  all  the  other  planets.  Owing  to 
the  considerable  eccentricity  of  its  orbit,  its  distance,  both 
from  the  sun  and  from  the  earth,  varies  in  a  larger  propor- 
tion than  does  that  of  the  other  outer  planets. 

At  the  most  favorable  oppositions,  its  distance  from  the 
earth  is  about,  0.38  of  the  astronomical  unit,  or,  in  round 
numbers,  57,000,000  kilometres  (35,000,000  of  miles). 
This  is  greater  than  the  least  distance  of  Venus,  but*we 
can  nevertheless  obtain  a  better  view  of  Mars  under  these 
circumstances  than  of  Venus,  because  when  the  latter  is 
nearest  to  us  its  dark  hemisphere  is  turned  toward  us, 
while  in  the  case  of  Mars  and  of  the  outer  planets  the 
hemisphere  turned  toward  us  at  opposition  is  fully  illumi- 
nated by  the  sun. 

The  period  of  revolution  of  Mars  around  the  sun  is  a 
little  less  than  two  years,  or,  more  exactly,  687  days.  The 
successive  oppositions  occur  at  intervals  of  two  years  and 
one  or  two  months,  the  earth  having  made  during  this  in- 
terval a  little  more  than  two  revolutions  around  the  sun, 
and  the  planet  Mars  a  little  more  than  one.  The  dates  of 


234  ASTRONOMY. 

several  past  and  future  oppositions  are  shown  in  the  fol- 
lowing table: 

1881 December  26th. 

1884 January  31st. 

1886 March  6th. 

Owing  to  the  unequal  motion  of  the  planet,  arising  from 
the  eccentricity  of  its  orbit,  the  intervals  between  succes- 
sive oppositions  vary  from  two  years  and  one  month  to  two 
years  and  two  and  a  half  months. 

Mars  necessarily  exhibits  phases,  but  they  are  not  so  well 
marked  as  in  the  case  of  Venus,  because  the  hemisphere 
which  it  presents  to  the  observer  on  the  earth  is  always 
more  than  half  illuminated.  The  greatest  phase  occurs 
when  its  direction  is  90°  from  that  of  the  sun,  and  even 
then  six  sevenths  of  its  disk  is  illuminated,  like  that  of  the 
moon,  three  days  before  or  after  full  moon.  The  phases 
of  Mars  were  observed  by  GALILEO  in  1610. 

notation  of  Mars. — The  early  telescopic  observers  noticed  that  the 
disk  of  Mars  did  not  appear  uniform  in  color  and  brightness,  but 
had  a  variegated  aspect.  In  1666  Dr.  ROIJEHT  HOOKE  found  that 
the  markings  on  Mart  were  permanent  and  moved  around  in  such  a 
way  as  to  show  that  the  planet  revolved  on  its  axis.  The  markings 
given  in  his  drawings  can  be  traced  at  the  present  day,  and  are 
made  use  of  to  determine  the  exact  period  of  rotation  of  the  planet. 
So  well  is  the  rotation  fixed  by  them  that  the  astronomer  can  now 
determine  the  exact  number  of  times  the  planet  has  rotated  on  its 
axis  since  these  old  drawings  were  made.  The  period  has  been 
found  to  be  24h  37m  22s -7,  a  result  which  appears  certain  to  one  or 
two  tenths  of  a  second.  It  is  therefore  less  than  an  hour  greater 
than  the  period  of  rotation  of  the  earth. 

Surface  of  Mars. — The  most  interesting  result  of  these  markings 
on  Mart  is  the  probability  that  its  surface  is  diversified  by  land  and 
water,  covered  by  an  atmosphere,  and  altogether  very  similar  to  the 
surface  of  the  earth.  Some  portions  of  the  surface  are  of  a  decided 
red  color,  and  thus  give  rise  to  the  well-known  fiery  aspect  of  the 
planet.  Other  parts  are  of  a  greenish  hue,  and  are  therefore  sup- 
posed to  be  seas.  The  most  striking  features  are  two  brilliant  white 


THE  PLANET  MARS.  235 

regions,  one  lying  around  each  pole  of  the  planet.  It  has  been  sup- 
posed that  this  appearance  is  due  to  immense  masses  of  snow  and 
ice  surrounding  the  poles.  If  this  were  so,  it  would  indicate  that 
the  processes  of  evaporation,  cloud  formation,  and  condensation  of 
vapor  into  rain  and  snow  go  on  at  the  surface  of  Mars  as  at  the  sur- 
face of  the  earth.  A  certain  amount  of  color  is  given  to  this  theory 
by  supposed  changes  in  the  magnitude  of  these  ice-caps.  But  the 
problem  of  establishing  such  changes  is  one  of  extreme  difficulty. 
The  only  way  in  which  an  adequate  idea  of  this  difficulty  can  be 
formed  is  by  the  student  himself  looking  at  Man  through  a  telescope. 
If  he  will  then  note  how  hard  it  is  to  make  out  the  different 
shades  of  light  and  darkness  on  the  planet,  and  how  they  must  vary  in 
aspect  under  different  conditions  of  clearness  in  our  own  atmosphere, 
he  will  readily  perceive  that  much  evidence  is  necessary  to  establish 
great  changes.  All  we  can  say,  therefore,  is  that  the  formation  of 
the  ice-caps  in  winter  and  their  melting  in  summer  has  some  evi- 
dence in  its  favor,  but  is  not  yet  completely  proven. 

SATELLITES  OF  MAES. 

Until  the  year  1877  Mars  was  supposed  to  have  no  satellites,  none 
having  ever  been  seen  in  the  most  powerful  telescopes.  But  in 
August  of  that  year  Professor  HALL,  of  the  Naval  Observatory, 
instituted  a  systematic  search  with  the  great  equatorial,  which 
resulted  in  the  discovery  of  two  such  objects. 

These  satellites  are  by  far  the  smallest  celestial  bodies  known.  It  is 
of  course  impossible  to  measure  their  diameters,  as  they  appear  in 
the  telescope  only  as  points  of  light.  The  outer  satellite  is  probably 
about  six  miles  and  the  inner  one  about  seven  miles  in  diameter. 
The  outer  one  was  seen  with  the  telescope  at  a  distance  from  the 
earth  of  7,000,000  times  this  diameter.  The  proportion  would  be 
that  of  a  ball  two  inches  in  diameter  viewed  at  a  distance  equal  to 
that  between  the  cities  of  Boston  and  New  York.  Such  a  feat  of 
telescopic  seeing  is  well  fitted  to  give  an  idea  of  the  power  of  modern 
optical  instruments. 

Professor  HALL  found  that  the  outer  satellite,  which  he  called 
Deimos,  revolves  around  the  planet  in  30h  16m,  and  the  inner  one, 
called  Phobos,  in  7h  38m.  The  latter  is  o;nly  5800  miles  from  the 
centre  of  Mars,  and  less  than  4000  miles  from  its  surface.  It  would 
therefore  be  almost  possible  with  one  of  our  telescopes  on  the  sur- 
face of  Mars  to  see  an  object  the  size  of  a  large  animal  on  the 
satellite. 

This  short  distance  and  rapid  revolution  make  the  inner  satellite 


236 


ASTRONOMY. 


of  Mars  one  of  the  most  interesting  bodies  with  which  we  are  ac- 
quainted. It  performs  a  revolution  in  its  orbit  in  less  than  half  the 
time  that  Mars  revolves  on  its  axis.  In  consequence,  to  the  inhab- 
itants of  Mars  it  would  seem  to  rise  in  the  west  and  set  in  the  east. 
It  will  be  remembered  that  the  revolution  of  the  moon  around  the 
earth  and  of  the  earth  on  its  axis  are  both  from  west  to  east ;  but  the 


FIG.  70.— TELESCOPIC  VIEW  OP  MARS. 

latter  revolution  being  the  more  rapid,  the  apparent  diurnal  motion 
of  the  moon  is  from  east  to  west.  In  the  case  of  the  inner  satellite 
of  Mars,  however,  this  is  reversed,  and  it  therefore  appears  to  move 
in  the  actual  direction  of  its  orbital  motion.  The  rapidity  of  its 
phases  is  also  equally  remarkable.  It  is  less  than  two  hours  from 
new  moon  to  first  quarter,  and  so  on.  Thus  the  inhabitants  of  Mars 
may  see  their  inner  moon  pass  through  all  its  phases  from  new  to 
full  and  again  to  new  in  a  single  night. 


CHAPTER  VI. 
THE  MINOR  PLANETS. 

the  solar  system  was  first  mapped  out  in  its  true 
proportions  by  COPERNICUS  and  KEPLER,  only  six  primary 
planets  were  known;  namely,  Mercury,  Venus,  the  Earth, 
Mars,  Jupiter,  and  Saturn.  These  succeeded  each  other 
according  to  a  nearly  regular  law,  as  we  have  shown  in 
Chapter  L,  except  that  between  Mars  and  Jupiter  a  gap 
was  left  where  an  additional  planet  might  be  inserted, 
and  the  order  of  distances  be  thus  made  complete.  It  was 
therefore  supposed  by  the  astronomers  of  the  seventeenth 
and  eighteenth  centuries  that  a  planet  might  be  found  in 
this  region.  A  search  for  this  object  was  instituted  to- 
ward the  end  of  the  last  century,  but  before  it  had  made 
much  progress  a  planet  in  the  place  of  the  one  so  long 
expected  was  found  by  PIAZZI,  of  Palermo.  The  discov- 
ery was  made  on  the  first  day  of  the  present  century,  1801, 
January  1st. 

In  the  course  of  the  following  seven  years  the  astronom- 
ical world  was  surprised  by  the  discovery  of  three  other 
planets,  all  in  the  same  region,  though  not  revolving  in 
the  same  orbits.  Seeing  four  small  planets  where  one 
large  one  ought  to  be,  OLBERS  was  led  to  his  celebrated 
hypothesis  that  these  bodies  were  the  fragments  of  a  large 
planet  which  had  been  broken  to  pieces  by  the  action  of 
some  unknown  force. 


238     -  ASTRONOMY. 

A  generation  of  astronomers  now  passed  away  without 
the  discovery  of  more  than  these  four.  In  1845  a  fifth 
planet  of  the  group  was  found.  In  1847  three  more  were 
discovered,  and  discoveries  have  since  been  made  at  a  rate 
which  thus  far  shows  no  signs  of  diminution.  The  num- 
ber has  now  reached  225,  and  the  discovery  of  additional 
ones  seems  to  be  going  on  as  fast  as  ever.  The  frequent 
announcements  of  the  discovery  of  planets  which  appear 
in  the  public  prints  all  refer  to  bodies  of  this  group. 

The  minor  planets  are  distinguished  from  the  major 
ones  by  many  characteristics.  Among  these  we  may  men- 
tion their  small  size;  their  positions,  all  being  situated  be- 
tween the  orbits  of  Mars  and  Jupiter;  the  great  eccentrici- 
ties and  inclinations  of  their  orbits. 

Number  of  Small  Planets. — It  would  be  interesting  to  know  how 
many  of  these  planets  there  are  in  all,  but  it  is  as  yet  impossible  even 
to  guess  at  the  number.  As  already  stated,  fully  200  are  now 
known,  and  the  number  of  new  ones  found  every  year  ranges  from 
7  or  8  to  10  or  12.  If  ten  additional  ones  are  found  every  year  dur- 
ing the  remainder  of  the  century,  400  will  then  have  been  dis- 
covered. 

A  minor  planet  presents  no  sensible  disk,  and  therefore  looks  ex- 
actly like  a  small  star.  It  can  be  detected  only  by  its  motion  among 
the  surrounding  stars,  which  is  so  slow  that  hours  must  elapse  before 
it  can  be  noticed. 

Magnitudes. — It  is  impossible  to  make  any  precise  measurement  of 
the  diameters  of  the  minor  planets.  These  can,  however,  be  esti 
mated  by  the  amount  of  light  which  the  planet  reflects.  Supposing 
the  proportion  of  light  reflected  about  the  same  as  in  the  case  of  the 
larger  planets,  it  is  estimated  that  the  diameters  of  the  three  or  four 
largest,  which  are  those  first  discovered,  range  between  300  and  600 
kilometres,  while  the  smallest  are  probably  from  20  to  50  kilometres 
in  diameter.  The  average  diameter  of  all  that  are  known  is  perhaps 
less  than  150  kilometres;  that  is,  scarcely  more  than  one  hundredth 
that  of  the  earth.  The  volumes  of  solid  bodies  vary  as  the  cubes  of 
their  diameters;  it  might  therefore  take  a  million  of  these  planets  to 
make  one  of  the  size  of  the  earth. 


THE  MINOR  PLANETS. 


Form  of  Orbits.  —  The  orbits  of  the  minor  planets  are  much  more 
eccentric  than  those  of  the  larger  ones;  their  distance  from  the  sun 
therefore  varies  very  widely. 

Origin  of  the  Minor  Planets.  —  The  question  of  the  origin  of  these 
bodies  was  long  one  of  great  interest.  The  features  which  we  have 
described  associate  themselves  very  naturally  with  the  hypothesis 
of  OLBERS,  that  we  here  have  the  fragments  of  a  single  large  planet 
which  in  the  beginning  revolved  in  its  proper  place  between  the 
orbits  of  Mars  and  Jupiter.  No  support  has  been  given  to  OLBERS' 
hypothesis  by  subsequent  investigations,  and  it  is  no  longer  consid- 
ered by  astronomers  to  have  any  foundation.  So  far  as  can  be  judged, 
these  bodies  have  been  revolving  around  the  sun  as  separate  planets 
ever  since  the  solar  system  itself  was  formed. 


CHAPTER  VII. 
JUPITER  AND  HIS  SATELLITES. 

THE  PLANET  JUPITER. 

Jupiter  is  much  the  largest  planet  in  the  system.  His 
mean  distance  is  nearly  800,000,000  kilometres  (480,000,- 
000  miles).  His  diameter  is  140,000  kilometres,  corre- 
sponding to  a  mean  apparent  diameter,  as  seen  from  the 
sun,  of  36*. 5.  His  linear  diameter  is  about  -fa,  his  surface 
is  rjT)  and  his  volume  y^  that  of  the  sun.  His  mass  is 
Y^I-J,  and  his  density  is  thus  nearly  the  same  as  the  sun's; 
viz.,  0.24  of  the  earth's.  He  rotates  on  his  axis  in 
9h  55m  20". 

He  is  attended  by  four  satellites,  which  were  discovered 
by  GALILEO  on  January  7th,  1610.  He  named  them,  in 
honor  of  the  MEDICIS,  the  Medicean  stars.  They  are 
now  known  as  Satellites  I,  II,  III,  and  IV,  I  being  the 
nearest. 

The  surface  of  Jupiter  has  been  carefully  studied  with 
the  telescope,  particularly  within  the  past  twenty  years. 
Although  further  from  us  than  Mars,  the  details  of  his 
disk  are  much  easier  to  recognize.  The  most  characteristic 
features  are  given  in  the  drawings  appended.  These 
features  are,  first,  the  dark  bands  of  the  equatorial 
regions,  and,  secondly,  the  cloud-like  forms  spread  over 
nearly  the  whole  surface.  At  the  limb  all  these  details 
become  indistinct,  and  finally  vanish,  thus  indicating  a 


JUPITER  AND  HIS  SATELLITES.  241 

highly  absorptive  atmosphere.  The  light  from  the  centre 
of  the  disk  is  twice  as  bright  as  that  from  the  poles.  The 
bands  can  be  seen  with  instruments  no  more  powerful 
than  those  used  by  GALILEO,  yet  he  makes  no  mention  of 
them. 

The  color  of  the  bands  is  reddish.  The  position  of  the 
bands  varies  in  latitude,  and  the  shapes  of  the  limiting 
curves  also  change  from  day  to  day;  but  in  the  main  they 
remain  as  permanent  features  of  the  region  to  which  they 
belong.  Two  such  bands  are  usually  visible,  but  often 


FIG.  71.— TELESCOPIC  VIEW  OF  JUPITER  AND  HIS  SATELLITES. 

more  are  seen.  HERSCHEL,  in  the  year  1793,  attributed 
the  aspects  of  the  bands  to  zones  of  the  planet's  atmos- 
phere more  tranquil  and  less  filled  with  clouds  than  the  re- 
maining portions,  so  as  to  permit  the  true  surface  of  the 
planet  to  be  seen  through  these  zones,  while  the  prevailing 
clouds  in  the  other  regions  give  a  brighter  tint  to  these 
latter.  The  color  of  the  bands  seems  to  vary  from  time  to 
time,  and  their  bordering  lines  sometimes  alter  with  such 
rapidity  as  to  show  that  these  borders  are  formed  of  some- 
thing like  clouds. 

The  clouds  themselves  can  easily  be  seen  at  times,  and 


242  ASTRONOMY. 

they  have  every  variety  of  shape,  sometimes  appearing  as 
brilliant  circular  white  masses,  but  oftener  they  are  similar 
in  form  to  a  series  of  white  cumulus  clouds  such  as  are 
frequently  seen  piled  up  near  the  horizon  on  a  summer's 
day.  The  bands  themselves  seem  frequently  to  be  veiled 
over  with  something  like  the  thin  cirrus  clouds  of  our  at- 
mosphere. 


FIG.  72.— TELESCOPIC  VIEW  OF  JUPITER.  WITH  A    SATELLITE  AND  ITS  SHADOW 
SEEN  ON  THE  DISK. 


Such  clouds  can  be  tolerably  accurately  observed,  and  may  be  used 
to  determine  the  rotation-time  of  the  planet.  These  observations 
show  that  the  clouds  have  often  a  motion  of  their  own,  which  is  also 
evident  from  other  considerations. 

The  following  results  of  observation  of  spots  situated  in  various 
regions  of  the  planet  will  illustrate  this; 


JUPITER  AND  HIS  SATELLITES. 


243 


h.  m.  8. 

CASSINI 1665,    rotation-time  =  9  56  00 

=  9  55  40 

=  9  50  48 

=  9  56  56 

=  9  55  26 


HERSCHEL 1778, 

HERSCHEL 1779, 

SCHROETER 1785, 

BEER  and  MADLER  .  1835, 


AIRY 1835, 

SCHMIDT 1862, 


=  9    55    21 
=  9    55    29 


Fro.  73. 

THE  SATELLITES  OF  JUPITER. 

Motions  of  the  Satellites. — The  four  satellites  move  about  Jupiter 
from  west  to  east  in  nearly  circular  orbits.  When  one  of  these 
satellites  passes  between  the  sun  and  Jupiter,  it  casts  a  shadow  upon 
Jupiter's  disk  (see  Fig.  73)  precisely  as  the  shadow  of  our  moon  is 


244  ASTRONOMY. 

thrown  upon  the  earth  in  a  solar  eclipse.  If  the  satellite  passes 
through  Jupiter's  own  shadow  in  its  revolution,  an  eclipse  of  this 
satellite  takes  place.  If  it  passes  between  the  earth  and  Jupiter,  it 
is  projected  upon  Jupiter' 8  disk,  and  we  have  a  transit;  if  Jupiter  is 
between  the  earth  and  the  satellite,  an  occultation  of  the  latter  oc- 
curs. All  these  phenomena  can  be  seen  with  a  common  telescope, 
and  the  times  of  observation  are  all  found  predicted  in  the  Nautical 
Almanac.  These  shadows  being  seen  black  upon  Jupiter's  surface, 
show  that  this  planet  shines  by  reflecting  the  light  of  the  sun. 

Telescopic  Appearance  of  the  Satellites. — Under  ordinary  circum- 
stances, the  satellites  of  Jupiter  are  seen  to  have  disks;  that  is,  not 
to  be  mere  points  of  light.  Under  very  favorable  conditions,  mark- 
ings have  been  seen  on  these  disks. 

The  satellites  completely  disappear  from  telescopic  view  when 
they  enter  the  shadow  of  the  planet.  This  seems  to  show  that 
neither  planet  nor  satellite  is  self  luminous  to  any  great  extent.  If 
the  satellite  were  self-luminous,  it  would  be  seen  by  its  own  light; 
and  if  the  planet  were  luminous,  the  satellite  might  be  seen  by  the  re- 
flected light  of  the  planet. 

The  motions  of  these  objects  are  connected  by  two  curious  and 
important  relations  discovered  by  LA  PLACE,  and  expressed  as  fol- 
lows: 

I.  The  mean  motion  of  t7ie  first  satellite  added  to  twice  the  mean  mo- 
tion of  the  third  is  exactly  equal  to  three  times  the  mean  motion  of  the 
second. 

II.  If  to  the  mean  longitude  of  the  first  satellite  we  add  twice  tJt#  mean 
longitude  of  the  third,  and  subtract  three  times  the  mean  longitude  of  the 
second,  the  difference  is  always  180°. 

The  first  of  these  relations  is  shown  in  the  following  table  of  the 
mean  daily  motions  of  the  satellites: 

Satellite  I  in  one  day  moves 203°. 4890 

"       II      "             "           1010.3748 

"     III     "             "           50°. 3177 

"      IV     "            "          21°.5711 

Motion  of  Satellite  1 203°.4890 

Twice  that  of  Satellite  III. .  100°. 6354 


Sum 304°.  1 244 

Three  times  motion  of  Satellite  II 304°.  1244 

Observations  showed  that  this  condition  was  fulfilled  as  exactly  as 
possible,  but  the  discovery  of  LA  PLACE  consisted  in  showing  that  if 
the  approximate  coincidence  of  the  mean  motions  was  once  estab- 


JUPITER  AND  HIS  SATELLITES. 


lished,  they  could  never  deviate  from  exact  coincidence  with  the 
law.  The  case  is  analogous  to  that  of  the  moon,  which  always 
presents  the  same  face  to  us  and  which  always  will,  since  the  rela- 
tion being  once  approximately  true,  it  will  become  exact  and  ever 
remain  so. 

The  discovery  of  the  gradual  propagation  of  light  by  means  of 
these  satellites  has  already  been  described,  and  it  has  also  been  ex- 
plained that  they  are  of  use  in  the  rough  determination  of  longi- 
tudes. To  facilitate  their  observation,  the  Nautical  Almanac  gives 
complete  ephemerides  of  their  phenomena.  A  specimen  of  a  portion 
of  such  an  ephemeris  for  1865,  March  7th,  8th,  and  9th,  is  added. 
The  times  are  Washington  mean  times. 

1865— MARCH. 


d.     h.    m.      s. 

I 

Eclipse 

Disapp. 

7    18    27    38.5 

I 

Occult. 

Reapp. 

7    21     56 

III 

Shadow 

Ingress 

8      7    27 

III 

Shadow 

Egress 

8      9    58 

III 

Transit 

Ingress 

8    12    31 

~  II 

Eclipse 

Disapp. 

8    13      1    22.7 

1  III 

Transit 

Egress 

8    15      6 

II 

Eclipse 

Reapp. 

8    15    24    11.1 

II 

Occult. 

Disapp. 

8    15    27 

I 

Shadow 

Ingress 

8    15    43 

I 

Transit 

Ingress 

8    16    58 

I 

Shadow 

Egress 

8    17    57 

II 

Occult. 

Reapp. 

8    17    59 

I 

Transit 

Egress 

8    19    13 

I 

Eclipse 

Disapp. 

9    12    55    59.4 

I 

Occult. 

Reapp. 

9    16    25 

Suppose  an  observer  near  New  York  City  to  have  determined  his 
local  time  accurately.  This  is  about  13m  faster  than  "Washington 
time.  On  1865.  March  8th,  he  would  look  for  the  reappearance  of 
II  at  about  15h34mof  his  local  time.  Suppose  he  observed  it  at 
15h  36m  22s. 7  of  his  time:  then  his  meridian  is  12m  118.6  east  of 
Washington.  The  difficulty  of  observing  these  eclipses  with  accu- 
racy, and  the  fact  that  the  aperture  of  the  telescope  employed  has  an 
important  effect  on  the  appeararcns  seen,  have  kept  this  method 
from  a  wide  utility,  which  it  at  first  seemed  to  promise. 


CHAPTER  VIII. 
SATURN  AND  ITS  SYSTEM. 

GENERAL  DESCRIPTION. 

Saturn  is  the  most  distant  of  the  major  planets  known 
to  the  ancients.  It  revolves  around  the  sun  in  29£  years, 
at  a  mean  distance  of  about  1,400,000,000  kilometres 
(883,000,000  miles).  The  angular  diameter  of  the  ball  of 
the  planet  is  about  16*.  2,  correspond  ing- to  a  true  diameter 
of  about  110,000  kilometres  (70,500  miles).  Its  diameter 
is  therefore  nearly  nine  times  and  its  volume  about  700 
times  that  of  the  earth.  It  is  remarkable  for  its  small 
density,  which,  so  far  as  known,  is  less  than  that  of  any 
other  heavenly  body,  and  even  less  than  that  of  water.  It 
revolves  on  its  axis  in  10h  14m  24s,  or  less  than  half  a  day. 

Saturn  is  perhaps  the  most  remarkable  planet  in  the 
solar  system,  being  itself  the  centre  of  a  system  of  its 
own,  altogether  unlike  anything  else  in  the  heavens.  Its 
most  noteworthy  feature  is  a  pair  of  rings  which  surround 
it  at  a  considerable  distance  from  the  planet  itself.  Out- 
side of  these  rings  revolve  no  less  than  eight  satellites, 
or  twice  the  greatest  number  known  to  surround  any  other 
planet.  The  planetj  rings,  and  satellites  are  altogether 
called  the  Saturnian  system.  The  general  appearance  of 
this  system,  as  seen  in  a  small  telescope,  is  shown  in  Fig.  74, 


SATURN  AND  ITS  SYSTEM.  247 

To  the  naked  eye  Saturn  is  of  a  dull  yellowish  color, 
shining  with  about  the  brilliancy  of  a  star  of  the  first  mag- 
nitude. It  varies  in  brightness,  however,  with  the  way  in 
which  its  ring  is  seen,  being  brighter  the  wider  the  ring 
appears.  It  comes  into  opposition  at  intervals  of  one  year 
and  from  twelve  to  fourteen  days.  The  following  are  the 


FIG.  74.— TELESCOPIC  VIEW  OP  THE  SATURNIAN  SYSTEM 

times  of  some  of  these  oppositions,  by  studying  which  one 
will  be  enabled  to  recognize  the  planet: 

1885 December  25th. 

1887 January  8th. 

1888 January  22d. 

During  these  years  it  will  be  best  seen  in  the  autumn 
and  winter. 

When  viewed  with  a  telescope,  the  physical  appearance 
of  the  ball  of  Saturn  is  quite  similar  to  that  of  Jupiter, 


248  ASTRONOMY. 

having  light  and  dark  belts  parallel  to  the  direction  of  its 
rotation. 

THE  RINGS  OF  SATURN. 

The  rings  arc  the  most  remarkable  and  characteristic  feature  of 
the  Saturnian  system.  Fig.  75  gives  two  views  of  the  ball  and  rings. 
The  upper  one  shows  one  of  their  aspects  as  actually  presented  in 
the  telescope,  and  the  lower  one  shows  what  the  appearance  would 
be  if  the  planet  were  viewed  from  ft  direction  at  right  angles  to  the 
plane  of  the  ring  (which  it  never  can  be  from  the  earth). 

The  first  telescopic  observers  of  &itnrn  were  unable  to  see  the 
rings  in  their  true  form,  and  were  greatly  perplexed  to  account 
for  the  appearance  which  the  planet  presented.  GALILEO  described 
the  planet  as  "  tri-corporate,"  the  two  ends  of  the  ring  having,  in  his 
imperfect  telescope,  the  appearance  of  a  pair  of  small  planets  at- 
tached to  the  central  one.  "On  each  side  of  old  Sitnm  were  ser- 
vitors who  aided  him  on  his  way."  This  supposed  discovery  was 
announced  to  his  friend  KEPLEH  in  this  logogriph: 

"smaismrmilmepoetalevmibimenugttaviras,"  which,  being  trans- 
posed, becomes — 

"  Altissimum  planetam  tergeminum  observavi"  (I  have  observed 
the  most  distant  planet  to  be  tri-form). 

The  phenomenon  constantly  remained  a  mystery  to  its  first  ob- 
server. In  1610  he  had  seen  the  planet  accompanied,  as  he  supposed, 
by  two  lateral  stars;  in  1612  the  latter  hail  vanished  and  the  central 
body  alone  remained.  After  that  GALILEO  ceased  to  observe  Saturn. 

The  appearances  of  the  ring  were  also  incomprehensible  to  HE- 
VELIUS,  GASSENDI,  and  others.  It  was  not  until  1655  (after  seven 
years  of  observation)  that  the  celebrated  HUYQIIENS  discovered  the 
true  explanation  of  the  remarkable  and  recurring  series  of  phenom- 
ena present  by  the  tri-corporate  planet. 

He  announced  his  conclusions  in  the  following  logogriph: 

"aaaaaa  ccccc  d  eeeee  g  h  iiiiiii  1111  mm.nnnnnnnnn  oooo  pp  q  rr  s 
ttttt  uuuuu,"  which,  when  arranged,  read — 

"  Annulo  cingitur,  tcnui,  piano,  nusquam  coherente,  ad  eclipticam 
inclinato"  (it  is  girdled  by  a  thin  plane  ring,  nowhere  touching,  in- 
clined to  the  ecliptic). 

This  description  is  complete  and  accurate. 

In  1675  it  was  found  by  CASSTNT,  that  what  HUYGHENS  had  seen 
as  a  single  ring  was  really  two.  A  division  extended  all  the  way 
around  neai  the  outer  edge  This  division  is  shown  in  the  figures. 

In  1850  the  Messrs    BOND   of  ILirv;inl  College  Observatory,  found 


SATURN  AND  ITS  SYSTEM.  249 


FIG.  75.— RING"  OF  SATURH, 


250  ASTRONOMY. 

that  there  was  a  third  ring,  of  a  dusky  and  nebulous  aspect,  inside  the 
other  two,  or  rather  attached  to  the  inner  edge  of  the  inner  ring.  It 
is  therefore  known  as  Bond's  dusky  ring.  It  had  not  been  before  fully 
described  owing  to  its  darkness  of  color,  which  made  it  a  difficult 
object  to  see  except  witli  a  good  telescope.  It  is  not  separated  from 
the  bright  ring,  but  seems  as  if  attached  to  it.  The  latter  shades  off 
toward  its  inner  edge,  and  merges  gradually  into  the  dusky  ring. 
The  latter  extends  about  half  way  from  the  inner  edge  of  the  bright 
ring  to  the  ball  of  the  planet. 

Aspect  of  the  Rings. — As  Saturn  revolves  around  the  sun,  the 
plane  of  the  rings  remains  parallel  to  itself.  That  is,  if  we  consider 
a  straight  line  passing  through  the  centre  of  the  planet,  perpendic- 
ular to  the  plane  of  the  ring,  as  the  axis  of  the  latter,  this  axis  will 
always  point  in  the  same  direction.  In  this  respect  the  motion  is 
similar  to  that  of  the  earth  around  the  sun.  The  ring  of  Hiturn  is 
inclined  about  27°  to  the  plane  of  its  orbit.  Consequently,  as  the 
planet  revolves  around  the  sun,  there  is  a  change  in  the  direction  in 
which  the  sun,  shines  upon  it  similar  to  that  which  produces  the 
change  of  seasons  upon  the  earth,  as  shown  in  Fig.  32. 

The  corresponding  changes  for  Saturn  are  shown  in  Fig  76.  Dur- 
ing each  revolution  of  Saturn  the  plane  of  the  ring  passes  through 
the  sun  twice.  This  occurred  in  the  years  1862  and  1878,  at  two 
opposite  points  of  the  orbit,  as  shown  in  the  figure.  At  two  other 
points,  midway  between  these,  the  sun  shines  upon  the  plane  of  the 
ring  at  its  greatest  inclination,  about  27°.  Since  the  earth  is  little 
more  than  one  tenth  as  far  from  the  sun  as  Saturn  is,  an  observer 
always  sees  Saturn  nearly,  but  not  quite,  as  if  he  were  upon  the  sun. 
Hence  at  certain  times  the  rings  of  Saturn  are  seen  edgeways;  while 
at  other  times  they  are  at  an  inclination  of  27°,  the  aspect  depending 
upon  the  position  of  the  planet  in  its  orbit.  The  following  are  the 
times  of  some  of  the  phases: 

1878,  February  7th.— The  edge  of  the  ring  was  turned  toward  the 
sun.  It  could  then  be  seen  only  as  a  thin  line  of  light. 

1885. — The  planet  having  moved  forward  90°,  the  south  side  of  the 
rings  may  be  seen  at  an  inclination  of  27°. 

1891,  December. — The  planet  having  moved  90°  further,  the  edge 
of  the  ring  is  again  turned  toward  the  sun. 

1899. — The  north  side  of  the  ring  is  inclined  toward  the  sun,  and 
is  seen  at  its  greatest  inclination. 

The  rings  are  extremely  thin  in  proportion  to  their  extent.  Con- 
sequently, when  their  edges  are  turned  toward  the  earth,  they  appear 
as  a  thin  line  of  light,  which  can  be  seen  only  with  powerful  tele- 
scopes. With  such  telescopes,  the  planet  appears  as  if  it  were 


SATURN  AND  ITS  SYSTEM. 


251 


pierced  through  by  a  piece  of  very  fine  wire,  the  ends  of  which  pro- 
ject on  each  side  more  than  the  diameter  of  the  planet.  It  has  fre- 
quently been  remarked  that  this  appearance  is  seen  on  one  side  of 
the  planet,  when  no  trace  of  the  ring  can  be  seen  on  the  other. 

There  is  sometimes  a  period  of  a  few  weeks  during  which  the 
plane  of  the  ring,  extended  outward,  passes  between  the  sun  and  the 
earth.  That  is,  the  sun  shines  on  one  side  of  the  ring,  while  the 
other  or  dark  side  is  turned  toward  the  earth.  In  this  case  it  seems 
to  be  established  that  only  the  edge  of  the  ring  is  visible.  If  this  be 


Fio.  76.— DIFFERENT  ASPECTS  OF  THE  RING  OF  SATURN  AS  SEEN  FROM  THE 
EARTH. 

so,  the  substance  of  the  rings  cannot  be  transparent  to  the  sun's  rays, 
else  it  would  be  seen  by  the  light  which  passes  through  it. 

Constitution  of  the  Rings  of  Saturn. — The  nature  of  these  objects 
has  been  a  subject  both  of  wonder  and  of  investigation  by  mathema- 
ticians and  astronomers  ever  since  they  were  discovered.  They  were 
at  first  supposed  to  be  solid  bodies;  indeed,  from  their  appearance  it 
was  difficult  to  conceive  of  them  as  anything  else.  The  question 
then  arose:  What  keeps  them  from  falling  on  the  planet?  It  was 
shown  by  LA  PLACE  that  a  homogeneous  and  solid  ring  surrounding 
the  planet  could  not  remain  in  a  state  of  equilibrium,  but  must  be 
precipitated  upon  the  central  ball  by  I  lie  smallest  disturbing  force. 


252 


A8THONOMT. 


It  is  now  established  beyond  reasonable  doubt  that  the  rings  do  not 
form  a  couliuuous  mass,  but  are  really  a  countless  multitude  of  small 
separate  particles,  each  of  which  revolves  on  its  own  account.  These 
satellites  are  individually  far  too  small  to  be  seen  in  any  telescope,  but 
so  numerous  that  when  viewed  from  the  distance  of  the  earth  they 
appear  as  a  continuous  mass,  like  particles  of  dust  floating  in  a 
sunbeam. 

SATELLITES  OF  SATURN. 

Outside  the  rings  of  Saturn  revolve  its  eight  satellites,  the  order 
and  discovery  of  which  are  shown  in  the  following  table: 


No. 

NAME 

Distance 
from 
Planet. 

Discoverer. 

Date  of  Discovery. 

1 
2 
3 
4 
5 
6 
7 
8 

Mimas 
Enceladus 
Tethys 
Dione 
Rhea 
Titan 
Hyperion 
Japetus 

3-3 
4-3 
5-3 

6-8 
9-5 
20-7 
26-8 
64-4 

Herschel 
Herschel 
Cassini 
Cassini 
Cassini 
Huyghens 
Bond 
Cassini 

1789,  September  17. 
1789,  August  28. 
1G84.   March. 
1684,  March. 
1672,  December  23. 
1655,  March  25. 
1848,  September  16. 
1671,  October. 

The  distances  from  the  planet  are  given  in  radii  of  the  latter.  The 
satellites  Mimas  and  Hyperion  are  visible  only  in  the  most  powerful 
telescopes.  The  brightest  of  all  is  Titan,  which  can  be  seen  in  a 
telescope  of  the  smallest  ordinary  size.  Japetus  has  the  remarkable 
peculiarity  of  appearing  nearly  as  bright  as  Titan  when  seen  west' of 
the  planet,  and  so  faint  as  to  be  visible  only  in  large  telescopes  when 
on  the  other  side.  This  appearance  is  explained  by  supposing  that, 
like  our  moon,  it  always  presents  the  same  face  to  the  planet,  and 
that  one  side  of  it  is  dark  and  the  other  side  light.  When  west  of 
the  planet,  the  bright  side  is  turned  toward  the  earth  and  the  satel- 
lite is  visible.  On  the  other  side  of  the  planet,  the  dark  side  is  turned 
toward  us,  and  it  is  nearly  invisible.  Most  of  the  remaining  five 
satellites  can  ordinarily  be  seen  with  telescopes  of  moderate  power. 


CHAPTER  IX. 
THE  PLANET  URANUS. 

Uranus  was  discovered  on  March  13th,  1781,  by  Sir 
WILLIAM  HERSCHEL  (then  an  amateur  observer)  with  a 
ten-foot  reflector  made  by  himself.  He  was  examining  a 
portion  of  the  sky  near  H  Geminorum,  when  one  of  the 
stars  in  the  field  of  view  attracted  his  notice  by  its  peculiar 
appearance.  On  further  scrutiny,  it  proved  to  have  a 
planetary  disk,  and  a  motion  of  over  2"  per  hour.  HERSCHEL 
at  first  supposed  it  to  be  a  comet  in  a  distant  part  of  its 
orbit,  and  under  this  impression  parabolic  orbits  were  com- 
puted for  it  by  various  mathematicians.  None  of  these, 
however,  satisfied  subsequent  observations,  and  it  was 
finally  determined  that  the  new  body  was  a  planet  revolv- 
ing in  a  nearly  circular  orbit.  We  can  scarcely  compre- 
hend now  the  enthusiasm  with  which  this  discovery  was 
received.  No  new  body  (save  comets)  had  been  added  to 
the  solar  system  since  the  discovery  of  the  third  satellite 
of  Saturn  in  1684,  and  all  the  major  planets  of  the  heavens 
had  been  known  for  thousands  of  years. 

Uranus  revolves  about  the  sun  in  84  years.  Its  apparent 
diameter  as  seen  from  the  earth  varies  little,  being  about 
3".  9.  Its  true  diameter  is  about  50,000  kilometres,  and  its 
figure  is  spheroidal. 

In  physical  appearance  it  is  a  small  greenish  disk  with- 


254  ASTZONOMY. 

out  markings.  It  is  possible  that  the  centre  of  the  disk  is 
slightly  brighter  than  the  edges.  At  its  nearest  approach 
to  the  earth,  it  shines  as  a  star  of  the  sixth  magnitude, 
and  is  just  visible  to  an  acute  eye  when  the  attention  is 
directed  to  its  place.  In  small  telescopes  with  low  powers, 
its  appearance  is  not  markedly  different  from  that  of  stars 
of  about  its  own  brilliancy. 

Sir  WILLIAM  HERSCHEL  suspected  that  Uranus  was  ac- 
companied by  six  satellites. 

Of  the  existence  of  two  of  these  satellites  there  has  never 
been  any  doubt.  No  one  of  the  other  four  satellites  de- 
scribed by  HERSCHEL  has  ever  been  seen,  and  he  was 
undoubtedly  mistaken  in  supposing  them  to  exist.  Two 
additional  ones  were  discovered  by  LASSELL  in  1847,  and 
they  are,  with  the  satellites  of  Mars,  the  faintest  objects  in 
the  solar  system.  Neither  of  them  is  identical  with  any  of 
the  missing  ones  of  HERSCHEL.  As  Sir  WILLIAM  HER- 
SCHEL had  suspected  six  satellites,  the  following  names  for 
the  true  satellites  are  generally  adopted  to  avoid  confusion: 

DAYS. 

I.  Aritl Period  =    2.520383 

II.  Umltriel "       =    4.144181 

III.  Titania,  HERSCHKL'S  (II.) "       =    8.705897 

IV.  Oberon,  HERSCHEL'S  (IV.) "       =  13.463269 

It  is  likely  that  Ariel  varies  in  brightness  on  different 
sides  of  the  planet,  and  the  same  phenomenon  has  also 
been  suspected  for  Titania. 

The  most  remarkable  feature  of  the  satellites  of  Uranus  is  that 
their  orbits  are  nearly  perpendicular  to  the  ecliptic  instead  of 
having  a  small  inclination  to  that  plane,  like  those  of  all  the  orbits 
of  both  planets  and  satellites  previously  known.  To  form  a  correct 
idea  of  the  position  of  tne  orbits,  we  must  imagine  them  tipped  over 
until  their  north  pole  is  nearly  8°  below  the  ecliptic,  instead  of  90° 


THE  PLANET  URANUS.  255 

above  it.  The  pole  of  the  orbit  which  should  be  considered  as  the 
north  one  is  that  from  which,  if  an  observer  look  down  upon  a  re- 
volving body,  the  latter  would  seem  to  turn  in  a  direction  opposite 
that  of  the  hands  of  a  watch.  When  the  orbit  is  tipped  over  more 
than  a  right  angle,  the  motion  from  a  point  in  the  direction  of  the 
north  pole  of  the  ecliptic  will  seem  to  be  the  reverse  of  this;  it  is 
therefore  sometimes  considered  to  be  retrograde.  This  term  is  fre- 
quently applied  to  the  motion  of  the  satellites  of  Uranus,  but  is 
rather  misleading,  since  the  motion,  being  nearly  perpendicular  to 
the  ecliptic,  is  not  exactly  expressed  by  the  term. 

The  four  satellites  move  in  the  same  plane.  This  fact  renders  it 
highly  probable  that  the  planet  Uranus  revolves  on  its  axis  in  the 
same  plane  with  the  orbits  of  the  satellites,  and  is  therefore  an  oblate 
spheroid  like  the  earth.  This  conclusion  is  founded  on  the  consid- 
eration that  if  the  planes  of  the  satellites  were  not  kept  together  by 
some  cause,  they  would  gradually  deviate  from  each  other  owing  to 
the  attractive  force  of  the  sun  upon  the  planet.  The  different  satel- 
lites would  deviate  by  different  amounts,  and  it  would  be  extremely 
improbable  that  all  the  orbits  would  at  any  time  be  found  in  the 
same  plane.  Since  we  see  them  in  the  same  plane,  we  conclude  that 
some  force  keeps  them  there,  and  the  oblateness  of  the  planet  would 
cause  such  a  force. 


CHAPTER  X. 
THE  PLANET  NEPTUNE. 

AFTER  the  planet  Uranus  had  been  observed  for  some 
thirty  years,  tables  of  its  motion  were  prepared  by  Bou- 
VARD.  He  had  as  data  available  for  this  purpose  not  only 
the  observations  since  1781,  but  also  observations  extend- 
ing back  as  far  as  1695,  in  which  the  planet  was  observed 
and  supposed  to  be  a  fixed  star.  As  one  of  the  chief  diffi- 
culties in  the  way  of  obtaining  a  theory  of  the  planet's 
motion  was  the  short  period  of  time  during  which  it  had 
been  regularly  observed,  it  was  to  be  supposed  that  these 
ancient  observations  would  materially  aid  in  obtaining 
jxact  accordance  between  the  theory  and  observation.  But 
it  was  found  that,  after  allowing  for  all  perturbations  pro- 
duced by  the  known  planets,  the  ancient  and  modern 
observations,  though  undoubtedly  referring  to  the  same 
object,  were  yet  not  to  be  reconciled  with  each  other,  but 
differed  systematically.  BOUVARD  was  forced  to  omit  the 
older  observations  in  his  tables,  which  were  published  in 
1820,  and  to  found  his  theory  upon  the  modern  observa- 
tions alone.  By  so  doing,  he  obtained  a  good  agreement 
between  theory  and  the  observations  of  the  few  years 
immediately  succeeding  1820. 

BOUVARD  seems  to  have  formulated  the  idea  that  a  pos- 
sible cause  for  the  discrepancies  noted  might  be  the  exist- 
ence of  an  unknown  planet,  but  the  meagre  data  at  his 
disposal  forced  him  to  leave  the  subject  untouched.  In 


THE  PLANET  NEPTUNE.  257 

1830  it  was  found  that  the  tables  which  represented  the 
motion  of  the  planet  well  in  1820-25  were  20"  in  error,  in 
1840  the  error  was  90*,  and  in  1845  it  was  over  120". 

These  progressive  and  systematic  changes  attracted  the 
attention  of  astronomers  to  the  subject  of  the  theory  of 
the  motion  of  Uranus.  The  actual  discrepancy  (120*)  in 
1845  was  not  a  quantity  large  in  itself.  Two  stars  of  the 
magnitude  of  Uranus,  and  separated  by  only  120*,  would 
be  seen  as  one  to  the  unaided  eye.  It  was  on  account  of 
its  systematic  and  progressive  increase  that  suspicion  was 
excited.  Several  astronomers  attacked  the  problem  in 
various  ways.  The  elder  STRUVE,  at  Pulkova,  prosecuted 
a  search  for  a  new  planet  along  with  his  double-star  obser- 
vations; BESS  EL,  at  Koenigsberg,  set  a  student  of  his  own, 
FLEMING,  at  a  new  comparison  of  observation  with  theory, 
in  order  to  furnish  data  for  a  new  determination;  ARAGO, 
then  Director  of  the  Observatory  at  Paris,  suggested  this 
subject  in  1845  as  an  interesting  field  of  research  to  LE 
VERRIER,  then  a  rising  mathematician  and  astronomer. 
Mr.  J.  C.  ADAMS,  a  student  in  Cambridge  University, 
England,  had  become  aware  of  the  problems  presented  by 
the  anomalies  in  the  motion  of  Uranus,  and  had  attacked 
this  question  as  early  as  1843.  In  October,  1845,  ADAMS 
communicated  to  the  Astronomer  Koyal  of  England  ele- 
ments of  a  new  planet  so  situated  as  to  produce  the  per- 
turbations of  the  motion  of  Uranus  which  had  actually 
been  observed.  Such  a  prediction  from  an  entirely  un- 
known student,  as  ADAMS  then  was,  did  not  carry  entire 
conviction  with  it.  A  series  of  accidents  prevented  the 
unknown  planet  being  looked  for  by  one  of  the  largest 
telescopes  in  England,  and  so  the  matter  apparently 
dropped.  It  may  be  noted,  however,  that  we  now  know 


258  ASTRONOMY. 

ADAMS'  elements  of  the  new  planet  to  have  been  so  near 
the  truth  that  if  it  had  been  really  looked  for  by  the  power- 
ful telescope  which  afterward  discovered  its  satellite,  it 
could  scarcely  have  failed  of  detection. 

BESSEL'S  pupil  FLEMING  died  before  his  work  was  done, 
and  BESSEL'S  researches  were  temporarily  brought  to  an 
end.  STRUVE'S  search  was  unsuccessful.  Only  LE  VER- 
RIER  continued  his  investigations,  and  in  the  most 
thorough  manner.  He  first  computed  anew  the  pertur- 
bation of  Uranus  produced  by  the  action  of  Jupiter  and 
Saturn.  Then  he  examined  the  nature  of  the  irregulari- 
ties observed.  These  showed  that  if  they  were  caused  by 
an  unknown  planet,  it  could  not  be  between  Sot  urn  and 
Uranus,  or  else  Saturn  would  have  been  more  affected 
than  was  the  case. 

The  new  planet  was  outside  of  Uranus  if  it  existed  at 
all,  and  as  a  rough  guide  BODE'S  law  was  invoked,  which 
indicated  a  distance  about  twice  that  of  Uranus.  In  the 
summer  of  1846  LE  VERRIER  obtained  complete  elements 
of  a  new  planet,  which  would  account  for  the  observed 
irregularities  in  the  motion  of  Uranus,  and  these  were 
published  in  France.  They  were  very  similar  to  those  of 
ADAMS,  which  had  been  communicated  to  Professor  CHAL- 
LIS,  the  Director  of  the  Observatory  of  Cambridge,  Eng- 
land. 

A  search  was  immediately  begun  by  CHALLIS  for  such 
an  object,  and  as  no  star-maps  were  at  hand  for  this  region 
of  the  sky,  he  began  mapping  the  surrounding  stars.  In 
so  doing  the  new  planet  was  actually  observed,  both  on 
August  4th  and  12th,  1846,  but  the  observations  remain- 
ing unreduced,  and  so  the  planetary  nature  of  the  object 
was  not  recognized. 


THE  PLANET  NEPTUNE.  259 

In  September  of  the  same  year  LE  VEBKIER  wrote  to 
Dr.  GALLE,  then  Assistant  at  the  Observatory  of  Berlin, 
asking  him  to  search  for  the  new  planet,  and  directing 
him  to  the  place  where  it  should  be  found.  By  the  aid 
of  an  excellent  star-chart  of  this  region,  which  had  just 
been  completed,  the  planet  was  found  September  23d,  1846. 

The  strict  rights  of  discovery  lay  with  LE  VEKRIEK, 
but  the  common  consent  of  mankind  has  always  credited 


Fio.  77. 

ADAMS  with  an  equal  share  in  the  honor  attached  to  this 
most  brilliant  achievement.  Indeed,  it  was  only  by  the 
most  unfortunate  succession  of  accidents  that  the  discovery 
did  not  attach  to  ADAMS'  researches.  One  thing  must  in 
fairness  be  said,  and  that  is  that  the  results  of  LE  VER- 
RIER,  which  were  reached  after  a  most  thorough  investi- 
gation of  the  whole  ground,  were  announced  with  an  en- 
tire confidence  which,  perhaps,  was  lacking  in  the  other 


260  ASTRONOMY. 

This  brilliant  discovery  created  more  enthusiasm  than 
even  the  discovery  of  Uranus,  as  it  was  by  an  exercise  of 
far  higher  qualities  that  it  was  achieved.  It  appeared  to 
savor  of  the  marvellous  that  a  mathematician  could  say 
to  a  working  astronomer  that  by  pointing  his  telescope  to 
a  certain  small  area,  within  it  should  be  found  a  new 
major  planet.  Yet  so  it  was. 

The  general  nature  of  the  disturbing  force  which  re- 
vealed the  new  planet  may  be  seen  by  Fig.  77,  whicli 
shows  the  orbits  of  the  two  planets,  and  their  respective 
motions  between  1781  and  1840.  The  inner  orbit  is  that 
of  Uranus,  the  outer  one  that  of  Neptune.  The  arrows 
passing  from  the  former  to  the  latter  show  the  directions 
of  the  attractive  force  of  Neptune.  It  will  be  seen  that 
the  two  planets  were  in  conjunction  in  the  year  1822. 
Since  that  time  Uranus  has,  by  its  more  rapid  motion, 
passed  more  than  90°  beyond  Neptune,  and  will  continue 
to  increase  its  distance  from  the  latter  until  the  begin- 
ning of  the  next  century. 

Our  knowledge  regarding  Neptune  is  mostly  confined  to 
a  few  numbers  representing  the  elements  of  its  motion. 
Its  mean  distance  is  more  than  4,000,000,000  kilometres 
(2,775,000,000  miles);  its  periodic  time  is  164.78  years; 
its  apparent  diameter  is  2.6  seconds,  corresponding  to  a 
true  diameter  of  55,000  kilometres.  Gravity  at  its  surface 
is  about  nine  tenths  of  the  corresponding  terrestrial  surface 
gravity.  Of  its  rotation  and  physical  condition  nothing 
is  known.  Its  color  is  a  pale  greenish  blue.  It  is  attended 
by  one  satellite,  which  was  discovered  by  Mr.  LASSELL,  of 
England,  in  1847.  The  satellite  requires  a  telescope  of 
twelve  inches'  aperture  or  upward  to  be  well  seen. 


CHAPTER  XL 
THE  PHYSICAL  CONSTITUTION  OF  THE  PLANETS. 

IT  is  remarkable  that  the  eight  large  planets  of  the  solar 
system,  considered  with  respect  to  their  physical  constitu- 
tion as  revealed  by  the  telescope  and  the  spectroscope,  may 
be  divided  into  four  pairs,  the  planets  of  each  pair  having 
a  great  similarity,  and  being  quite  different  from  the  ad- 
joining pair. 

Mercury  and  Venus. — Passing  outward  from  the  sun,  the 
first  pair  we  encounter  will  be  Mercury  and  Venus.  The 
most  remarkable  feature  of  these  two  planets  is  a  negative 
rather  than  a  positive  one,  being  the  entire  absence  of  any 
certain  evidence  of  change  on  their  surfaces.  We  have  al- 
ready shown  that  Venus  has  a  considerable  atmosphere, 
while  there  is  no  evidence  of  any  such  atmosphere  around 
Mercury.  They  have  therefore  not  been  proved  alike  in 
this  respect,  yet,  on  the  other  hand,  they  have  not  been 
proved  different.  In  every  other  respect  than  this  the 
similarity  appears  perfect.  No  permanent  markings  have 
ever  been  certainly  seen  on  the  disk  of  either.  If,  as  is 
possible,  the  atmosphere  of  both  planets  is  filled  with  clouds 
and  vapor,  no  change,  no  openings,  and  no  formations 
among  these  cloud  masses  are  visible  from  the  earth.  When- 
ever either  of  these  planets  is  in  a  certain  position  relative 
to  the  earth  and  the  sun,  it  seemingly  presents  the  same 
appearance,  and  not  the  slightest  change  occurs  in  that 


262  ASTRONOMY. 

appearance  from  the  rotation  of  the  planet  on  its  axis, 
which  every  analogy  of  the  solar  system  leads  us  to  believe 
must  take  place. 

When  studied  with  the  spectroscope,  the  spectra  of  Mer- 
cury and  Venus  do  not  differ  strikingly  from  that  of  the 
sun.  This  would  seem  to  indicate  that  the  atmospheres  of 
these  planets  do  not  exert  any  decided  absorption  upon  the 
rays  of  light  which  pass  through  them  ;  or,  at  least,  they 
absorb  only  the  same  rays  which  are  absorbed  by  the  at- 
mosphere of  the  sun  and  by  that  of  the  earth.  The  one 
point  of  difference  is  that  the  lines  of  the  spectrum  pro- 
duced by  the  absorption  of  our  own  atmosphere  appear 
darker  in  the  spectrum  of  Venus.  If  this  were  so,  it 
would  indicate  that  the  atmosphere  of  Venus  is  similar  in 
constitution  to  that  of  our  earth,  because  it  absorbs  the 
same  rays.  But  the  means  of  measuring  the  darkness  of 
the  lines  are  as  yet  so  imperfect  that  it  is  impossible  to 
speak  with  certainty  on  a  point  like  this. 

The  Earth  and  Mars. — These  planets  are  distinguished 
from  all  the  others  in  that  their  visible  surfaces  are  mark- 
ed by  permanent  features,  which  show  them  to  be  solid, 
and  which  can  be  seen  from  the  other  heavenly  bodies.  It 
is  true  that  we  cannot  study  the  earth  from  any  other 
body,  but  we  can  form  a  very  correct  idea  how  it  would 
look  if  seen  in  this  way  (from  the  moon,  for  instance). 
Wherever  the  atmosphere  was  clear,  the  outlines  of  the 
continents  and  oceans  would  be  visible,  while  they  would 
be  invisible  where  the  air  was  cloudy. 

Now,  so  far  as  we  can  judge  from  observations  made  at 
so  great  a  distance,  never  much  less  than  forty  millions  of 
miles,  the  planet  Mars  presents  to  our  telescopes  very 
much  the  same  general  appearance  that  the  earth  would  if 


PHYSICAL  CONSTITUTION  Of1  THE  PLANETS.    263 

observed  from  an  equally  great  distance.  The  only  ex- 
ception is  that  ihe  visible  surface  of  Mars  is  seemingly  much 
less  obscured  by  clouds  than  that  of  the  earth  would  be.  In 
other  words,  that  planet  has  a  more  sunny  sky  than  ours. 
It  is,  of  course,  impossible  to  say  what  conditions  we  might 
find  could  we  take  a  much  closer  view  of  Mars :  all  we  can 
assert  is,  that  so  far  as  we  can  judge  from  this  distance, 
its  surface  is  like  that  of  the  earth. 

This  supposed  similarity  is  strengthened  by  the  spectro- 
scopic  observations. 

Jupiter  and  Saturn. — The  next  pair  of  planets  is  Jupi- 
ter and  Saturn.  Their  peculiarity  is  that  no  solid  crust 
or  surface  is  visible  from  without.  In  this  respect  they 
differ  from  the  earth  and  Mars,  and  resemble  Mercury 
and  Venus.  But  they  differ  from  the  latter  in  the  very 
important  point  that  constant  changes  can  be  seen  going 
on  at  their  surfaces.  The  preponderance  of  evidence  is 
in  favor  of  the  view  that  these  planets  have  no  solid 
crusts  whatever,  but  consist  of  masses  of  molten  matter, 
surrounded  by  envelopes  of  vapor  constantly  rising  from 
the  interior. 

This  view  is  further  strengthened  by  their  very  small 
specific  gravity,  which  can  be  accounted  for  by  supposing 
that  the  liquid  interior  is  nothing  more  than  a  compara- 
tively small  central  core,  and  that  the  greater  part  of  the 
bulk  of  each  planet  is  composed  of  vapor  of  small  density. 

That  the  visible  surfaces  of  Jupiter  and  Saturn  are  cov- 
ered by  some  kind  of  an  atmosphere  follows  not  only  from 
the  motion  of  the  cloud  forms  seen  there,  but  from  the 
spectroscopic  observations. 

Uranus  and  Neptune, — These  planets  have  a  strikingly 
similar  aspect  when  seen  through  a  telescope.  They  differ 


264  ASTRONOMY. 

from  Jupiter  and  Saturn  in  that  no  changes  or  variations 
of  color  or  aspect  can  be  made  out  upon  their  surfaces; 
and  from  the  earth  and  Mars  in  the  absence  of  any  perma- 
nent features.  Telescopically,  therefore,  we  might  classify 
them  with  Mercury  and  Venus,  but  the  spectroscope  re- 
veals a  constitution  entirely  different  from  that  of  any 
other  planets.  The  most  marked  features  of  their  spectra 
are  very  dark  bands,  evidently  produced  by  the  absorption 
of  dense  atmospheres.  Owing  to  the  extreme  faintness  of 
the  light  which  reaches  us  from  these  distant  bodies,  the 
regular  lines  of  the  solar  spectrum  are  entirely  invisible  in 
their  spectra,  yet  these  dark  bands  which  are  peculiar  to 
them  have  been  seen  by  several  astronomers. 

This  classification  of  the  eight  planets  into  pairs  is  ren- 
dered yet  more  striking  by  the  fact  that  it  applies  to  what 
we  have  been  able»to  discover  respecting  the  rotations  of 
these  bodies.  The  rotation  of  the  inner  pair,  Mercury 
and  Venus,  has  eluded  detection,  notwithstanding  their 
comparative  proximity  to  us.  The  next  pair,  the  earth 
and  Mars,  have  perfectly  definite  times  of  rotation, 
because  their  outer  surfaces  consist  of  solid  crusts,  every 
part  of  which  must  rotate  in  the  same  time.  The  next 
pair,  Jupiter  and  Saturn,  have  well-established  times 
of  rotation,  but  these  times  are  not  perfectly  definite, 
because  the  surfaces  of  these  planets  are  not  solid,  and  dif- 
ferent portions  of  their  mass  may  rotate  in  slightly  different 
times.  Jupiter  and  Saturn  have  also  in  common  a  very 
rapid  rate  of  rotation.  Finally,  the  outer  pair.  Uranus 
and  Neptune,  seem  to  be  surrounded  by  atmospheres  of 
such  density  that  no  evidence  of  rotation  can  be  gathered. 
Thus  it  seems  that  of  the  eight  planets  only  the  central 
four  have  yet  certainly  indicated  a  rotation  on  their  axes. 


CHAPTER  XII. 
METEORS. 

PHENOMENA  AND  CAUSES  OF  METEORS. 

DURING  the  present  century  evidence  has  been  collected 
that  countless  masses  of  matter,  far  too  small  to  be  seen 
with  the  most  powerful  telescopes,  are  moving  through 
the  planetary  spaces.  This  evidence  is  afforded  by  the 
phenomena  of  "aerolites,"  "meteors,"  and  "shooting- 
stars."  Although  these  several  phenomena  have  been  ob- 
served and  noted  from  time  to  time  since  the  earliest  his- 
toric era,  it  is  only  recently  that  a  complete  explanation 
has  been  reaehed. 

Aerolites. — Reports  of  the  falling  of  large  masses  of 
stone  or  iron  to  the  earth  have  been  familiar  to  antiqua- 
rian students  for  many  centuries.  The  problem  where 
such  a  body  could  come  from,  or  how  it  could  get  into  the 
atmosphere  to  fall  down  again,  formerly  seemed  so  nearly 
incapable  of  solution  that  it  required  some  credulity  to 
admit  the  facts.  When  the  evidence  became  so  strong  as 
to  be  indisputable,  theories  of  their  origin  began  to  be 
propounded.  One  theory  quite  fashionable  in  the  early 
part  of  this  century  was  that  they  were  thrown  from 
volcanoes  in  the  moon.  This  theory  has  little  to  sup- 
port it. 

The  proof  that  aerolites  did  really  fall  to  the  ground  first  became 
conclusive  by  the  fall  being  connected  with  other  more  familiar 
phenomena.  Nearly  every  one  who  is  at  all  observant  of  the 


266  ASTRONOMY. 

heavens  is  familiar  with  bolides,  or  fire-balls — brilliant  objects  having 
the  appearance  of  rockets,  which  are  occasionally  seen  moving  with 
great  velocity  through  the  upper  regions  of  the  atmosphere. 
Scarcely  a  year  passes  in  which  such  a  body  of  extraordinary  bril- 
liancy is  not  seen.  Generally  these  bodies,  bright  though  they  may 
be,  vanish  without  leaving  any  trace,  or  making  themselves  evident 
to  any  sense  but  that  of  sight.  But  on  rare  occasions  their  appearance 
is  followed  at  an  interval  of  several  minutes  by  loud  explosions  like 
the  discharge  of  a  battery  of  artillery.  The  fall  of  these  aerolites  is 
always  accompanied  by  light  and  sound,  though  the  light  may  be 
invisible  in  the  daytime. 

When  chemical  analysis  was  applied  to  aerolites,  they  were  proved 
to  be  of  extramundane  origin,  because  they  contained  chemical 
combinations  not  found  in  terrestrial  substances.  It  is  true  that  they 
contained  no  new  chemical  elements,  but  only  a  combination  of  the 
elements  which  are  found  on  the  earth.  These  combinations  are 
now  so  familiar  to  mineralogists  that  they  can  distinguish  an  aerolite 
from  a  mineral  of  terrestrial  origin  by  a  careful  examination.  One 
of  the  most  frequent  components  of  these  bodies  is  iron. 

Meteors. — Although  the  meteors  we  have  described  are  of  dazzling 
brilliancy,  yet  they  run  by  insensible  'gradations  into  phenomena, 
which  any  one  can  see  on  any  clear  night.  The  most  brilliant 
meteors  of  all  are  likely  to  be  seen  by  one  person  only  two  or  three 
times  in  his  life.  Meteors  having  the  appearance  and  brightness  of 
a  distant  rocket  may  be  seen  several  times  a  year.  Smaller  ones 
occur  more  frequently;  and  if  a  careful  watch  be  kept,  it  will  be 
found  that  several  of  the  faintest  class  of  all,  familiarly  known  as 
shooting-stars,  can  be  seen  on  every  clear  night.  We  can  draw  no 
distinction  between  the  most  brilliant  meteor  illuminating  the  whole 
sky,  and  perhaps  making  a  noise  like  thunder,  and  the  faintest 
shooting-star,  except  one  of  degree.  There  seems  to  be  every  grada- 
tion between  these  extremes,  so  that  all  should  be  traced  to  some 
common  cause. 

Cause  of  Meteors. — There  is  now  no  doubt  that  all  these  phenomena 
have  a  common  origin,  and  that  they  are  due  to  the  earth  encounter- 
ing innumerable  small  bodies  in  its  annual  course  around  the  sun. 
The  great  difficulty  in  connecting  meteors  with  these  invisible  bodies 
arises  from  the  brilliancy  and  rapid  disappearance  of  the  meteors. 
The  question  may  be  asked,  Why  do  they  burn  with  so  great  an  evolu- 
tion of  light  on  reaching  our  atmosphere?  To  answer  this  question 
we  must  have  recourse  to  the  mechanical  theory  of  heat.  Heat  is  a 
vibratory  motion  in  the  particles  of  solid  bodies  and  a  progressive 
motion  in  those  of  gases.  By  making  this  motion  more  rapid  we 


^ 


METEORS.  Xs[>  *    267 

make  the  body  warmer.  By  simply  blowing  air  against  any  com- 
bustible body  with  sufficient  velocity  it  can  be  set  on  fire,  and,  if 
incombustible,  the  body  will  be  made  red-hot  and  finally  melted. 
Experiments  to  determine  the  degree  of  temperature  thus  produced 
have  been  made  which  show  that  a  velocity  of  about  50  metres  per 
second  corresponds  to  a  rise  of  temperature  of  one  degree  Centi- 
grade. From  this  the  temperature  due  to  any  velocity  can  be  readily 
calculated  on  the  principle  that  the  increase  of  temperature  is  pro- 
portional to  the  "energy"  of  the  particles,  which  again  is  propor- 
tional to  the  square  of  the  velocity.  Hence  a  velocity  of  500  metres 
per  second  would  correspond  to  a  rise  of  100°  above  the  actual  tem- 
perature of  the  air,  so  that  if  the  latter  was  at  the  freezing-point  the 
body  would  be  raised  to  the  temperature  of  boiling  water.  A  velocity 
of  1500  metres  per  second  would  produce  a  red  heat. 

The  earth  moves  around  the  sun  with  a  velocity  of  about  30,000 
metres  per  second;  consequently  if  it  met  a  body  at  rest  the  concus- 
sion between  the  latter  and  the  atmosphere  would  correspond  to  a 
temperature  of  more  than  300,000°.  This  would  instantly  dissolve 
any  known  substance. 

It  must  be  remembered  that  when  we  speak  of  these  enormous 
temperatures,  we  are  to  consider  them  as  potential,  not  actual,  tem- 
peratures. We  do  not  mean  that  the  body  is  actually  raised  to  a 
temperature  of  300,000°,  but  only  that  the  air  acts  upon  it  as  if  it 
were  put  into  a  furnace  heated  to  this  temperature;  that  is,  it  is 
rapidly  destroyed  by  the  intensity  of  the  heat. 

This  potential  temperature  is  independent  of  the  density  of  the 
medium,  being  the  same  in  the  rarest  as  in  the  densest  atmosphere. 
But  the  actual  effect  on  the  body  is  not  so  great  in  a  rare  as  in  a 
dense  atmosphere.  Every  one  knows  that  he  can  hold  his  hand 
for  some  time  in  air  at  the  temperature  of  boiling  water.  The  rarer 
the  air  the  higher  the  temperature  the  hand  would  bear  without 
injury.  In  an  atmosphere  as  rare  as  ours  at  the  height  of  50  miles, 
it  is  probable  that  the  hand  could  be  held  for  an  indefinite  period, 
though  its  temperature  should  be  that  of  red-hot  iron;  hence  the 
meteor  is  not  consumed  so  rapidly  as  if  it  struck  a  dense  atmosphere 
with  planetary  velocity.  In  the  latter  case  it  would  probably  dis- 
appear like  a  flash  of  lightning. 

The  amount  of  heat  evolved  is  measured  not  by  that  which 
would  result  from  the  combustion  of  the  body,  but  by  the  vis  viva 
(energy  of  motion)  which  the  body  loses  in  the  atmosphere.  The 
student  of  physics  knows  that  motion,  when  lost,  is  changed  into  a 
definite  amount  of  heat.  If  we  calculate  the  amount  of  heat  which 
is  equivalent  to  the  energy  of  motion  of  a  pebble  having  a  velocity 


268  ASTRONOMY. 

of  20  miles  a  second,  we  shall  find  it  sufficient  to  raise  about  1300 
times  the  pebble's  weight  of  water  from  the  free/.ing  to  the  boiling 
point.  This  is  many  times  as  much  heat  as  could  result  from  burn- 
ing even  the  most  combustible  body. 

The  detonation  which  sometimes  accompanies  the  passage  of 
very  brilliant  meteors  is  not  caused  by  an  explosion  of  the  meteor, 
but  by  the  concussion  produced  by  its  rapid  motion  tli rough  our  at- 
mosphere. This  concussion  is  of  much  the  same  nature  as  that  pro- 
duced by  a  flash  of  lightning.  The  air  is  suddenly  condensed  in 
front  of  the  meteor,  while  a  vacuum  is  left  behind  it. 

The  invisible  bodies  which  produce  meteors  in  the  way  just  de- 
scribed have  been  called  meteoroids.  Meteoric  phenomena  depend 
very  largely  upon  the  nature  of  the  meteoroids.  and  the  direction  and 
velocity  with  which  they  are  moving  relatively  to  the  earth.  With 
very  rare  exceptions,  they  are  so  small  and  fusible  as  to  be  entirely 
dissipated  in  the  upper  regions  of  the  atmosphere.  Even  of  those 
so  hard  and  solid  as  to  produce  a  brilliant  light  and  the  loudest  deto- 
nation, only  a  small  proportion  reach  the  earth.  On  rare  occasions 
the  body  is  so  hard  and  massive  as  to  reach  the  earth  without  being 
entirely  consumed.  The  potential  heat  produced  by  its  passage 
through  the  atmosphere  is  then  all  expended  in  melting  and  destroy- 
ing its  outer  layers,  the  inner  nucleus  remaining  unchanged.  When 
such  a  body  first  strikes  the  denser  portion  of  the  atmosphere,  the 
resistance  becomes  so  great  that  the  body  is  generally  broken  to 
pieces  Hence  we  very  often  find  not  simply  a  single  aerolite,  but  a 
small  shower  of  them. 

Heights  of  Meteors.— Many  observations  have  been  made  to  deter- 
mine the  height  at  which  meteors  are  seen.  This  is  effected  by  two 
observers  stationing  themselves  several  miles  apart  and  mapping  out 
the  courses  of  such  meteors  as  they  can  observe.  In  the  case  of  very 
brilliant  meteors,  the  path  is  often  determined  with  considerable  pre- 
cision by  the  direction  in  which  it  is  seen  by  accidental  observers  in 
various  regions  of  the  country  over  which  it  passes  This  observa- 
tion is  nothing  but  a  simultaneous  determination  of  the  parallax  of  a 
meteor  as  seen  from  two  stations.  See  Fig.  17. 

Meteors  and  shooting-stars  commonly  commence  to  be  visible  at  a 
height  of  about  160  kilometres,  or  100  statute  miles.  The  separate 
results  vary  widely,  but  this  is  a  rough  mean  of  them.  They 
are  generally  dissipated  at  about  half  this  height,  and  therefore 
above  the  highest  atmosphere  which  reflects  the  rays  of  the  sun. 
From  this  it  may  be  inferred  that  the  earth's  atmosphere  rises  to  a 
height  of  at  least  160  kilometres.  This  is  a  much  greater  height  than 
it  was  formerly  supposed  to  have. 


METEORS.  269 


METEORIC  SHOWERS. 

As  already  stated,  the  phenomena  of  shooting-stars  may 
be  seen  by  a  careful  observer  on  almost  any  clear  night. 
In  general,  not  more  than  three  or  four  of  them  will  be 
seen  in  an  hour,  and  these  will  be  so  minute  as  hardly  to 
attract  notice.  But  they  sometimes  fall  in  such  numbers 
as  to  present  the  appearance  of  a  meteoric  shower.  On 
rare  occasions  the  shower  has  been  so  striking  as  to  fill  the 
beholders  with  terror.  The  ancient  and  mediaeval  records 
contain  many  accounts  of  these  phenomena  which  have  been 
brought  to  light  through  the  researches  of  antiquarians. 

It  has  long  been  known  that  some  showers  of  this  class 
occur  at  an  interval  of  about  a  third  of  a  century.  One 
was  observed  by  HUMBOLDT,  on  the  Andes,  on  the  night  of 
November  12th,  1799,  lasting  from  two  o'clock  until  day- 
light. A  great  shower  was  seen  in  this  country  in  1833, 
and  is  well  known  to  have  struck  the  negroes  of  the 
Southern  States  with  terror.  The  theory  that  the  showers 
occur  at  intervals  of  34  years  was  propounded  by  OLBERS, 
who  predicted  a  return  of  the  shower  in  1867.  This  pre- 
diction was  completely  fulfilled,  but  instead  of  appearing 
in  the  year  1867  only,  it  was  first  noticed  in  1866.  On  the 
night  of  November  13th  of  that  year  a  remarkable  shower 
was  seen  in  Europe,  while  on  the  corresponding  night  of 
the  year  following  it  was  again  seen  in  this  country,  and, 
in  fact,  was  repeated  for  two  or  three  years,  gradually  dy- 
ing away. 

The  occurrence  of  a  shower  of  meteors  evidently  shows 
that  the  earth  encounters  a  swarm  of  meteoroids.  The  re- 
currence at  the  same  time  of  the  year,  when  the  earth  is 
in  the  same  point  of  its  orbit,  shows  that  the  earth  meets 


270  ASTRONOMY. 

the  swarm  at  the  same  point  in  successive  years.  All  the 
meteoroids  of  the  swarm  must  of  course  be  moving  in  the 
same  direction,  else  they  would  soon  be  widely  scattered. 
This  motion  is  connected  with  the  radiant  point,  a  well- 
marked  feature  of  a  meteoric  shower. 

Kadiant  Point. — Suppose  that,  during  a  meteoric  shower,  we  mark 
the  path  of  each  meteor  on  a  star-map,  as  in  the  figure.  If  we  con- 
tinue the  paths  backward  in  a  straight  line,  we  shall  find  that  they 
all  meet  near  one  and  the  same  point  of  the  celestial  sphere;  that  is, 
they  move  as  if  they  all  radiated  from  this  point.  The  latter  is, 
therefore,  called  the  radiant  point.  In  the  figure  the  lines  do  not  all 
pass  accurately  through  t lie  same  point.  This  is  owing  to  the  un- 
avoidable errors  made  in  marking  out  the  path. 

It  is  found  that  the  radiant  point  is  always  in  the  same  position 
among  the  stars,  wherever  the  observer  may  be  situated,  and  that 
as  the  utars  apparently  move  toward  the  west,  tfie  radiant  point  moves 
with  them. 

The  radiant  point  is  due  to  the  fact  that  the  meteoroids  which 
strike  the  earth  during  a  shower  are  all  moving  in  the  same  direc- 
tion. Their  motions  will  all  be  parallel;  hence  when  the  bodies 
strike  our  atmosphere  the  paths  described  by  them  in  their  passage 
will  all  be  parallel  straight  lines.  A  straight  line  seen  by  an  ob- 
server at  any  point  is  projected  as  a  great  circle  of  the  celestial 
sphere,  of  which  the  observer  supposes  himself  to  be  the  centre.  If 
we  draw  a  line  from  the  observer  parallel  to  the  paths  of  the  meteors, 
the  direction  of  that  line  will  represent  a  point  of  the  sphere  through 
which  all  the  paths  will  seem  to  pass;  this  will,  therefore,  be  the 
radiant  point  in  a  meteoric  shower. 

Orbits  of  Meteoric  Showers. — From  what  has  just  been  said  it  will 
be  seen  that  the  position  of  the  radiant  point  indicates  the  direction 
in  which  the  meteoroids  move  relatively  to  the  earth.  If  we  also 
knew  the  velocity  with  which  they  arc  really  moving  in  space,  we 
could  make  allowance  for  the  motion  of  the  earth,  and  thus  deter- 
mine the  direction  of  their  actual  motion  in  space.  If  we  know  this, 
it  is  possible  to  calculate  the  actual  direction  and  velocity  of  the 
meteoric  swarm  in  space.  Having  this  direction  and  velocity,  the 
orbit  of  the  swarm  around  the  sun  admits  of  being  calculated. 

Kelations  of  Meteors  and  Comets, — The  velocity  of  the 
meteoroids  does  not  admit  of  being  determined  from  obser- 


METEORS.  271 

yation.     One  element  necessary  for  determining  the  orbits 
of  these  bodies  is,  therefore,  wanting.     In  the  case  of  the 


FIG.  78.— RADIANT  POINT  OF  METEORIC  SH 


showers  of  1799,   1833,  and  1866,  commonly  called  the 
November  showers,  this  element  is  given  by  the  time  of 


272  ASTRONOMY. 

revolution  around  the  sun.  Since  the  showers  occur  at 
intervals  of  about  a  third  of  a  century,  it  is  highly  proba- 
ble this  is  the  periodic  time  of  the  swarm  around  th  esun. 
The  periodic  time  being  known,  the  velocity  at  any  dis- 
tance from  the  sun  admits  of  calculation  from  the  theory 
of  gravitation.  Thus  we  have  all  the  data  for  determining 
the  real  orbits  of  the  group  of  meteors  around  the  sun. 

The  calculations  necessary  for  this  purpose  were  made 
by  LE  VERRIER  and  other  astronomers  shortly  after  the 
great  shower  of  1866.  The  following  was  the  orbit  as 
given  by  LE  VERRIER: 

Period  of  revolution 33.25  years. 

Eccentricity  of  orbit 0.9044. 

Least  distance  from  the  sun 0.9890. 

Inclination  of  orbit 165°  19'. 

Longitude  of  the  node 51°  18'. 

Position  of  the  perihelion (near  the  node). 

The  publication  of  this  orbit  brought  to  the  attention  of 
the  world  an  extraordinary  coincidence  which  had  never 
before  been  suspected.  In  December,  1865,  a  faint  tele- 
scopic comet  was  discovered.  Its  orbit  was  calculated  as 
follows : 

Period  of  revolution 33.18  years. 

Eccentricity  of  orbit 0  9054. 

Least  distance  from  the  sun 0.9765. 

Inclination  of  orbit 162°  42'. 

Longitude  of  the  node 51°  26'. 

Longitude  of  the  perihelion 42°  24'. 

The  publication  of  the  cometary  orbit  and  that  of  the 
orbit  of  the  meteoric  group  were  made  independently  with- 
in a  few  days  of  each  other  by  two  astronomers,  neither  of 
whom  had  any  knowledge  of  the  work  of  the  other.  Corn- 
Daring  them,  the  result  is  evident.  The  swarms  of  meteor- 


METEORS.  273 

oids  which  cause  the  November  showers  move  in  the  same 
orbit  with  this  comet. 

The  comet  passed  its  perihelion  in  January,  1866.  The 
most  striking  meteoric  shower  commenced  in  the  following 
November,  and  was  repeated  during  several  years.  It 
seems,  therefore,  that  the  meteoroids  which  produce  these 
showers  follow  after  TEMPEL'S  comet,  moving  in  the  same 
orbit  with  it.  This  shows  a  curious  relation  between 
comets  and  meteors,  of  which  we  shall  speak  more  fully  in 
the  next  chapter.  When  this  fact  was  brought  out,  the 
question  naturally  arose  whether  the  same  thing  might  not 
be  true  of  other  meteoric  showers. 

Other  Showers  of  Meteors. — Although  the  November 
showers  (which  occur  about  November  14)  are  the  only 
ones  so  brilliant  as  to  strike  the  ordinary  eye,  it  has  long 
been  known  that  there  are  other  nights  of  the  year  (nota- 
bly August  10)  in  which  more  shooting-stars  than  usual 
are  seen,  and  in  which  the  large  majority  radiate  from  one 
point  of  the  heavens.  This  shows  conclusively  that  they 
arise  from  swarms  of  meteoroids  moving  together  around 
the  sun. 

The  Zodiacal  Light. — If  we  observe  the  western  sky  during  the 
winter  or  spring  months,  about  the  end  of  the  evening  twilight,  we 
shall  see  a  stream  of  faint  light,  a  little  like  the  Milky  Way,  rising 
obliquely  from  the  west,  and  directed  along  the  ecliptic  toward  a 
point  south-west  from  the  zenith.  This  is  called  the  zodiacal  light. 
It  may  also  be  seen  in  the  east  before  daylight  in  the  morning  during 
the  autumn  months,  and  has  sometimes  been  traced  all  the  way 
across  the  heavens.  Its  origin  is  still  involved  in  obscurity,  but  it 
seems  probable  that  it  arises  from  an  extremely  thin  cloud  either  of 
meteoroids  or  of  semi-gaseous  matter  like  that  composing  the  tail  of 
a  comet,  spread  all  around  the  sun  inside  the  earth's  orbit.  Its 
spectrum  is  probably  that  of  reflected  sunlight,  a  result  which  gives 
color  to  the  theory  that  it  arises  from  a  cloud  of  meteoroids  revolv- 
ing round  the  sun. 


CHAPTER  XIII. 

COMETS. 
ASPECT  OF  COMETS. 

COMETS  are  distinguished  from  the  planets  botli  by  their 
aspects  and  their  motions.  They  come  into  view  without 
anything  to  herald  their  approach,  continue  in  sight  for  a 
few  weeks  or  months,  and  then  gradually  vanish  in  the 
distance.  They  are  commonly  considered  us  composed  of 
three  parts:  the  nucleus,  the  coma  (or  hair),  and  the  tail. 

The  nucleus  of  a  comet  is,  to  the  naked  eye,  a  point  of 
light  resembling  a  star  or  planet.  Viewed  in  a  telescope, 
it  generally  has  a  small  disk,  but  shades  off  so  gradually 
that  it  is  difficult  to  estimate  its  magnitude.  In  large 
comets  it  is  sometimes  several  hundred  miles  in  diameter. 

The  nucleus  is  always  surrounded  by  a  mass  of  foggy 
light,  which  is  called  the  coma.  To  the  naked  eye  the 
nucleus  and  coma  together  look  like  a  star  seen  through  a 
mass  of  thin  fog,  which  surrounds  it  with  a  sort  of  halo. 
The  nucleus  and  coma  together  are  generally  called  the 
head  of  the  comet. 

The  tail  of  the  comet  is  simply  a  continuation  of  the 
coma  extending  out  to  a  great  distance,  and  always  di- 
rected away  from  the  sun.  It  has  the  appearance  of  a 
stream  of  milky  light,  which  grows  fainter  and  broader 
as  it  recedes  from  the  head.  Like  the  coma  it  shades  off 
so  gradually  that  it  is  impossible  to  fix  any  boundaries  to 
it.  The  length  of  the  tail  varies  from  2°  or  3°  to  90°  or 


COMETS.  275 

more.  Generally  the  more  brilliant  the  head  of  the  comet, 
the  longer  and  brighter  is  the  tail. 

The  above  description  applies  to  comets  which  can  be 
plainly  seen  by  the  naked  eye.  Half  a  dozen  telescopic 
comets  may  be  discovered  in  a  single  year,  while  one  of  the 
brighter  class  may  not  be  seen  for  ten  years  or  more. 

When  comets  are  studied  with  a  telescope,  it  is  found 
that  they  are  subject  to  extraordinary  changes  of  structure. 


FIG.  79.— TELESCOPIC  COMET  WITHOUT          FIG.  80.— TELESCOPIC  COMET  WITH 
A  NUCLEUS.  A  NUCLEUS. 

To  understand  these  changes,  we  must  begin  by  saying  that 
comets  do  not,  like  the  planets,  revolve  around  the  sun  in 
nearly  circular  orbits,  but  always  in  orbits  so  elongated 
that  the  comet  is  visible  in  only  a  very  small  part  of  its 
course.  See  page  278,  Fig.  82.) 

THE  VAPOROUS  ENVELOPES. 

If  a  comet  is  very  small,  it  may  undergo  no  changes  of  aspect 
during  its  entire  course.  If  it  is  an  unusually  bright  one.  a  bow 
surrounding  the  nucleus  on  the  side  toward  the  sun  will  develop 
as  the  comet  approaches  the  sun.  This  bow  will  gradually  rise  up 
and  spread  out  on  all  sides,  finally  assuming  the  form  of  a  semi- 
circle having  the  nucleus  in  its  centre,  or,  to  speak  with  more  pre- 
cision, the  form  of  a  parabola  having  the  nucleus  near  its  focus. 
The  two  ends  of  this  parabola  will  extend  out  further  and  further 
so  as  to  form  a  part  of  the  tail,  and  finally  be  lost  in  it.  Other  bows 


276  ASTRONOMY. 

will  successively  form  around  the  nucleus,  all  slowly  rising  from  it 
like  clouds  of  vapor.  These  distinct  vaporous  masses  are  called  the 
envelopes :  they  shade  off  gradually  into  the  coma  so  as  to  be  with 
difficulty  distinguished  from  it,  and  indeed  maybe  considered  as  part 
of  it.  These  appearances  are  apparently  caused  by  masses  of  vapor 
streaming  up  from  that  side  of  the  nucleus  nearest  the  sun,  and  grad- 
ually spreading  around  the  comet  on  each  side.  The  form  of  a  bow 
is  not  the  real  form  of  the  envelopes,  but  only  the  apparent  one  in 
which  we  see  them  projected  against  the  background  of  the  sky. 
Perhaps  their  forms  can  be  best  imagined  by  supposing  the  sun  to 
be  directly  above  the  comet,  and  a  fountain,  throwing  a  liquid  hori- 
zontally on  all  sides,  to  be  built  upon  that  part  of  the  comet  which 
is  uppermost.  Such  a  fountain  would  throw  its  water  in  the  form 
of  a  sheet,  falling  on  all  sides  of  the  cometic  nucleus,  but  not  touch- 


Fio.  81.— FORMATION  OF  ENVELOPES. 

ing  it.  Two  or  three  vapor  surfaces  of  this  kind  are  sometimes  seen 
around  the  comet,  the  outer  one  enclosing  each  of  the  inner  ones, 
but  no  two  touching  each  other. 

THE  PHYSICAL  CONSTITUTION  OF  COMETS. 

To  tell  exactly  what  a  comet  is,  we  should  be  able  to  show  how  all 
the  phenomena  it  presents  would  follow  from  the  properties  of  mat- 
ter, as  we  learn  them  at  the  surface  of  the  earth.  This,  however,  no 
one  has  been  able  to  do,  many  of  the  phenomena  being  such  as  we 
should  not  expect  from  the  known  constitution  of  matter.  All  we 
can  do,  therefore,  is  to  present  the  principal  characteristics  of  comets, 
as  shown  by  observation,  and  to  explain  what  is  wanting  to  reconcile 
these  characteristics  with  the  known  properties  of  matter. 

In  the  first  place,  all  comets  which  have  been  examined  with  the 
spectroscope  show  a  spectrum  composed,  in  part  at  least,  of  bright 
lines  or  bands.  The  positions  and  characters  of  these  bands  leave  no 


COMETS.  277 

doubt  that  carbon,  hydrogen,  and  nitrogen,  and  probably  oxygen  are 
present  in  the  cometary  matter.  More  than  twenty  comets  have  been 
examined  since  the  invention  of  the  spectroscope  and  all  agree  in 
giving  the  same  evidence.  In  some  recent  comets  sodium  has  also 
been  discovered. 

In  the  last  chapter  it  was  shown  that  swarms  of  minute  particles 
called  meteoroids  follow  certain  comets  in  their  orbits.  This  is  no 
doubt  true  of  all  comets.  We  can  only  regard  these  meteoroids  as 
fragments  or  debris  of  the  comet.  On  this  theory  a  telescopic  comet 
which  has  no  nucleus  is  simply  a  cloud  of  these  minute  bodies.  The 
nucleus  of  the  brighter  comets  may  either  be  a  more  condensed  mass 
of  such  bodies  or  it  may  be  a  solid  or  liquid  body  itself. 

If  the  reader  has  any  difficulty  in  reconciling  this  theory  of  de- 
tached particles  with  the  view  already  presented,  that  the  envelopes 
from  which  the  tail  of  the  comet  is  formed  consist  of  layers  of  vapor, 
he  must  remember  that  vaporous  masses,  such  as  clouds,  fog,  and 
smoke,  are  really  composed  of  minute  separate  particles  of  water  or 
carbon. 

Formation  of  the  Comet's  Tail. — The  tail  of  the  comet  is  not  a  per- 
manent appendage,  but  is  composed  of  the  masses  of  vapor  which 
we  have  already  described  as  ascending  from  the  nucleus,  and  after- 
ward moving  away  from  the  sun.  The  tail  which  we  see  on  one 
evening  is  not  absolutely  the  same  we  saw  the  evening  before,  a  por- 
tion of  the  latter  having  been  dissipated,  while  new  matter  has  taken 
its  place,  as  with  the  stream  of  smoke  from  a  steamship.  The 
motion  of  the  vaporous  matter  which  forms  the  tail  being  always 
away  from  the  sun,  there  seems  to  be  a  repulsive  force  exerted  by 
the  sun  upon  it.  The  form  of  the  comet's  tail,  on  the  supposition 
that  it  is  composed  of  matter  driven  away  from  the  sun  with  a  uni- 
formly accelerated  velocity,  has  been  several  times  investigated,  and 
found  to  represent  the  observed  form  of  the  tail  so  nearly  as  to 
leave  little  doubt  of  its  correctness.  We  may,  therefore,  regard  it  as 
an  observed  fact  that  the  vapor  which  rises  from  the  nucleus  of  the 
comet  is  repelled  by  the  sun  instead  of  being  attracted  toward  it,  as 
larger  masses  of  matter  are. 

No  adequate  explanation  of  this  repulsive  force  has  ever  been 
given. 

MOTIONS  OF  COMETS. 

Previous  to  the  time  of  NEWTON,  no  certain  knowledge  respecting 
the  actual  motions  of  comets  in  the  heavens  had  been  acquired,  ex- 
cept that  they  did  not  move  around  the  sun  in  ellipses  like  the  planets. 


278  ASTRONOMY. 

When  NEWTON  investigated  the  mathematical  results  of  the  theory 
of  gravitation,  he  found  that  a  body  moviug  under  the  attraction  of 
the  sun  might  describe  either  of  the  three  conic  sections,  the  ellipse, 
parabola,  or  hyperbola.  Bodies  moving  in  an  ellipse,  as  the  planets, 
would  complete  their  orbits  at  regular  intervals  of  time,  according 
to  laws  already  laid  down.  But  if  the  body  moved  in  a  parabola  or 
an  hyperbola,  it  would  never  return  to  the  sun  after  once  passing  it, 
but  would  move  off  to  infinity.  It  was,  therefore,  very  natural  to 
conclude  that  comets  might  be  bodies  which  resemble  the  planets  in 
moving  under  the  sun's  attraction,  but  which,  instead  of  describing 


FIG.  82.— ELLIPTIC  AND  PARABOLIC  ORBITS. 

an  ellipse  in  regular  periods,  like  the  planets,  move  in  parabolic  or 
hyperbolic  orbits,  and  therefore  only  approach  the  sun  a  single  time 
during  their  whole  existence. 

This  theory  is  now  known  to  be  essentially  true  for  most  of  the 
observed  comets.  A  few  are  indeed  found  to  be  revolving  around 
the  sun  in  elliptic  orbits,  which  differ  from  those  of  the  planets  only 
in  being  much  more  eccentric.  But  the  greater  number  which  have 
been  observed  have  receded  from  the  sun  in  orbits  which  we  are  un- 
able to  distinguish  from  parabolas,  though  it  is  possible  they  ma}7  be 
extremely  elongated  ellipses.  Comets  are  therefore  divided  with  re- 


COMETS. 


sped  to  their  motions  into  two  classes:  (Aperiodic  comets,  which  are 
known  to  move  in  elliptic  orbits,  and  to  return  to  the  sun  at  fixed  in- 
tervals; and  (2)  parabolic  comets,  apparently  moving  in  parabolas, 
never  to  return. 

The  first  discovery  of  the  periodicity  of  a  comet  was  made  by  HAL- 
LEY  in  connection  with  the  great  comet  of  1682.  Examining  the  records 
of  past  observations,  he  found  that  a  comet  moving  in  nearly  the 
same  orbit  with  that  of  1682  had  been  seen  in  1607,  and  still  another 
in  1531.  He  was  therefore  led  to  the  conclusion  that  these  three 
comets  were  really  one  and  the  same  object,  returning  to  the  sun  at 
intervals  of  about  75  or  76  years.  He  therefore  predicted  that  it 
would  appear  again  about  the  year  1758.  The  coinet  was  first  seen 


FIG.  83.— ORBIT  OF  HALLEY'S  COMET. 

on  Christmas-day,  1758,  and  passed  its  perihelion  March  12th,  1759, 
only  one  month  before  the  predicted  time.  At  present  it  is  possible 
to  predict  the  places  of  some  of  the  best  known  periodic  comets 
almost  as  accurately  as  the  positions  of  the  planets. 

We  give  a  figure  showing  the  position  of  the  orbit  of  HALLEY'S 
comet  relative  to  the  orbits  of  the  four  outer  planets.  It  attained  its 
greatest  distance  from  the  sun,  far  beyond  the  orbit  of  Neptune, 
about  the  year  1873,  and  then  commenced  its  return  journey.  The 
figure  shows  the  position  of  the  comet  in  1874.  It  was  then  far  be- 
yond the  reach  of  the  most  powerful  telescope,  but  its  distance  and 
direction  admit  of  being  calculated  with  so  much  precision  that  a 
telescope  could  be  pointed  at  it  at  any  required  moment. 


280  ASTRONOMY. 

REMARKABLE  COMETS. 

It  is  familiarly  known  that  bright  comets  were  in  former 
years  objects  of  great  terror,  being  supposed  to  presage 
the  fall  of  empires,  the  death  of  monarchs,  the  approach 
of  earthquakes,  wars,  pestilence,  and  every  other  calamity 
which  could  afflict  mankind.  In  showing  the  entire 
groundlessness  of  such  fears,  science  has  rendered  one  of 
its  greatest  benefits  to  mankind. 

In  1456  the  comet  known  as  HALLEY'S,  appearing 
when  the  Turks  were  making  war  on  Christendom,  caused 


D 

STERN  DJROKT 
ROESE  SACHBN 
TRAV. 
GOTT 

WlRDsWoL 


Fio.  84.— MEDAL  OF  THE  GREAT  COMET  OP  1680-81. 

such  terror  that  Pope  CALIXTUS  ordered  prayers  to  be 
offered  in  the  churches  for  protection  against  it.  This 
is  supposed  to  be  the  origin  of  the  popular  myth  that  the 
Pope  once  issued  a  bull  against  the  comet. 

The  number  of  comets  visible  to  the  naked  eye,  so  far  as 
recorded,  has  generally  ranged  from  twenty  to  forty  in  a 
century.  Only  a  small  portion  of  these,  however,  have 
been  so  bright  as  to  excite  universal  notice. 

Comet  of  1680.— One  of  the  most  remarkable  of  these 
brilliant  comets  is  that  of  1680.  It  inspired  such  terror 
that  a  medal,  of  which  we  present  a  figure,  was  struck 
upon  the  Continent  of  Europe  to  quiet  apprehension.  A 
free  translation  of  the  inscription  is  :  "The  star  threatens 


COMETS.  281 

evil  things ;  trust  only !  God  will  turn  them  to  good."  * 
What  makes  this  comet  especially  remarkable  in  history 
is  that  NEWTON  calculated  its  orbit,  and  showed  that  it 
moved  around  the  sun  in  a  conic  section,  in  obedience  to 
the  law  of  gravitation. 

Great  Comet  of  1811. — It  has  a  period  of  over  3000 
years,  and  its  aphelion  distance  is  about  40,000,000,000 
miles. 

Great  Comet  of  1843. — One  of  the  most  brilliant  comets 
which  have  appeared  during  the  present  century  was  that 
of  February,  1843.  It  was  visible  in  full  daylight  close  to 
the  sun.  Considerable  terror  was  caused  in  some  quar- 
ters lest  it  might  presage  the  end  of  the  world,  which  had 
been  predicted  for  that  year  by  MILLER.  At  perihelion  it 
passed  nearer  the  sun  than  any  other  body  has  ever  been 
known  to  pass,  the  least  distance  being  only  about  one 
fifth  of  the  sun's  semi  diameter.  With  a  very  slight 
change  of  its  original  motion,  it  would  have  actually  fallen 
into  the  sun. 

Great  Comet  of  1858. — Another  comet  remarkable  for 
the  length  of  time  it  remained  visible  was  that  of  1858. 
It  is  frequently  called  after  the  name  of  DON  ATI,  its  first 
discoverer.  No  comet  visiting  our  neighborhood  in  recent 
times  has  afforded  so  favorable  an  opportunity  for  study- 
ing its  physical  constitution.  Its  greatest  brilliancy 
occurred  about  the  beginning  of  October,  when  its  tail  was 
40°  in  length  and  10°  in  breadth  at  its  outer  end.  Its  period 
is  1950  years. 

*  The  student  should  notice  the  care  which  the  author  of  the  in- 
scription has  taken  to  make  it  consolatory,  to  make  it  rhymo,  and 
to  give  implicitly  the  year  of  the  comet  by  writing  certain  Roman 
numerals  larger  than  the  other  letters. 


FIG.  85.— Dwuii'i  OOMBT  OP  1868. 


COMETS.  283 

Great  Comet  of  1882. — It  is  yet  too  soon  to  speak  of  the 
results  of  the  observations  on  this  magnificent  object.  Its 
splendor  will  not  soon  be  forgotten  by  those  who  have 
seen  it. 

Encke's  Comet  and  the  Eesisting  Medium. — Of  telescopic  comets, 
that  which  has  been  most  investigated  by  astronomers  is  known  as 
ENCKK'S  comet.  Its  period  is  between  three  and  four  years.  Viewed 
with  a  telescope,  it  is  not  different  in  any  respect  from  other  tele- 
scopic comets,  appearing  simply  as  a  mass  of  foggy  light,  somewhat 
brighter  near  one  side.  .Under  the  most  favorable  circumstances,  it 
is  just  visible  to  the  naked  eye.  The  circumstance  which  has  lent 
most  interest  to  this  comet  is  that  the  observations  which  have  been 
made  upon  it  seem  to  indicate  that  it  is  gradually  approaching  the 
sun.  ENCKE  attributed  this  change  in  its  orbit  to  the  existence  in 
space  of  a  resisting  medium,  so  rare  as  to  have  no  appreciable  effect 
upon  the  motion  of  the  planets,  and  to  be  felt  only  by  bodies  of  ex- 
treme tenuity,  like  the  telescopic  comets.  The  approach  of  the 
comet  to  the  sun  is  shown,  not  by  direct  observation,  but  only  by  a 
gradual  diminution  of  the  period  of  revolution.  It  will  be  many 
centuries  before  thif  period  would  be  so  far  diminished  that  the 
comet  would  actually  touch  the  sun. 

If  the  change  in  the  period  of  this  comet  were  actually  due  to  the 
cause  which  ENCKE  supposed,  then  other  faint  comets  of  the  same 
kind  ought  to  be  subject  to  a  similar  influence.  But  the  investiga- 
tions which  have  been  made  in  recent  times  on  these  bodies  show  no 
deviation  of  the  kind.  It  might,  therefore,  be  concluded  that  the 
change  in  the  period  of  ENCKE'S  comet  must  be  due  to  some  other 
cause.  There  is,  however,  one  circumstance  which  leaves  us  in 
doubt.  ENCKE'S  comet  passes  nearer  the  sun  than  any  other  comet 
of  short  period  which  has  been  observed  with  sufficient  care  to  de- 
cide the  question.  It  may,  therefore,  be  supposed  that  the  resisting 
medium,  whatever  it  may  be,  is  densest  near  the  sun,  and  does  not 
extend  out  far  enough  for  the  other  comets  to  meet  it.  The  question 
is  one  very  difficult  to  settle.  The  fact  is  that  all  comets  exhibit 
slight  anomalies  in  their  motions  which  prevent  us  from  deducing 
conclusions  from  them  with  the  same  certainty  that  we  should  from 
those  of  the  planets.  One  of  the  chief  difficulties  in  investigating 
the  orbits  of  comets  with  all  rigor  is  due  to  the  difficulty  of  obtaining 
accurate  positions  of  the  centre  of  so  ill-defined  an  object  as  the 
nucleus. 


PART   III. 

THE  UNIVERSE  AT  LARGE. 


INTRODUCTION. 

IN  our  studies  of  the  heavenly  bodies,  we  have  hitherto 
been  occupied  almost  entirely  with  those  of  the  solar  sys- 
tem. Although  this  system  comprises  the  bodies  which 
are  most  important  to  us,  yet  they  form  only  an  insignifi- 
cant part  of  creation.  Besides  the  earth  on  which  we 
dwell,  only  seven  of  the  bodies  of  the  solar  system  are 
plainly  visible  to  the  naked  eye,  whereas  some  2000  stars 
or  more  can  be  seen  on  any  clear  night. 

The  material  universe,  as  revealed  by  the  telescope,  con- 
sists principally  of  shining  bodies,  many  millions  in  num- 
ber, a  few  of  the  nearest  and  brightest  of  which  are  visible 
to  the  naked  eye  as  stars.  They  extend  out  as  far  as  the 
most  powerful  telescope  can  penetrate,  and  no  one  knows 
how  much  farther.  Our  sun  is  simply  one  of  these  stars, 
and  does  not,  so  far  as  we  know,  differ  from  its  fellows  in  any 
essential  characteristic.  From  the  most  careful  estimates, 
it  is  rather  less  bright  than  the  average  of  the  nearer  stars, 
and  overpowers  them  by  its  brilliancy  only  because  it  is  so 
much  nearer  to  us. 

The  distance  of  the  stars  from  each  other,  and  therefore 
from  the  sun,  is  immensely  greater  than  any  of  the  dis- 
tances which  we  have  hitherto  had  to  consider  in  the  solar 


286  ASTRONOMY. 

system.  In  fact,  the  nearest  known  star  is  about  seven 
thousand  times  as  far  as  the  planet  Neptune.  If  we  sup- 
pose the  orbit  of  this  planet  to  be  represented  by  a  child's 
hoop,  the  nearest  star  would  be  three  or  four  miles  away. 
We  have  no  reason  to  suppose  that  contiguous  stars  are,  on 
the  average,  nearer  than  this,  except  in  special  cases  where 
they  are  collected  together  in  clusters. 

The  total  number  of  the  stars  is  estimated  by  millions,  and 
they  are  probably  separated  by  these  wide  intervals.  It 
follows  that,  in  going  from  the  sun  to  the  nearest  star,  we 
would  be  simply  taking  one  step  in  the  universe.  The 
most  distant  stars  visible  in  great  telescopes  are  probably 
several  thousand  times  more  distant  than  the  nearest  one, 
and  we  do  not  know  what  may  lie  beyond. 

The  point  we  wish  principally  to  impress  on  the  reader 
in  this  connection  is  that,  although  the  stars  and  planets  pre- 
sent to  the  naked  eye  so  great  a  similarity  in  appearance, 
there  is  the  greatest  possible  diversity  in  their  distances 
and  characters.  The  planets,  though  many  millions  of 
miles  away,  are  comparatively  near  us,  and  form  a  little 
family  by  themselves,  which  is  called  the  solar  system. 
The  fixed  stars  are  at  distances  incomparably  greater — the 
nearest  star  being  thousands  of  times  more  distant  than 
the  farthest  planet.  The  planets  are,  so  far  as  we  can  see, 
worlds  somewhat  like  this  on  which  we  live,  while  the  stars 
are  suns,  generally  larger  and  brighter  than  our  own. 
Each  star  may,  for  aught  we  know,  have  planets  revolving 
around  it,  but  their  distance  is  so  immense  that  the  largest 
planets  will  remain  invisible  with  the  most  powerful  tele- 
scopes man  can  ever  hope  to  construct. 

The  classification  of  the  heavenly  bodies  thus  leads  us  to 
this  curious  conclusion.  Our  sun  is  one  of  the  family  of 


THE   UNIVERSE  AT  LARGE.  287 

stars,  the  other  members  of  which  stud  the  heavens  at 
night,  or,  in  other  words,  the  stars  are  suns  like  that  which 
makes  the  day.  The  planets,  though  they  look  like  stars, 
are  not  such,  but  bodies  more  like  the  earth. 

The  great  universe  of  stars,  including  the  creation  in  its 
largest  extent,  is  called  the  stellar  system)  or  stellar 
universe.  We  have  first  to  consider  how  it  looks  to  the 
naked  eye. 


CHAPTER  I. 
CONSTELLATIONa 

GENERAL  ASPECT  OF  THE  HEAVENS. 

WHEN  we  view  the  heavens  with  the  unassisted  eye,  the 
stars  appear  to  be  scattered  nearly  at  random  over  the 
surface  of  the  celestial  vault.  The  only  deviation  from  an 
entirely  random  distribution  which  can  be  noticed  is  a  cer- 
tain grouping  of  the  brighter  ones  into  constellations. 
A  few  stars  are  comparatively  much  brighter  than  the  rest, 
and  there  is  every  gradation  of  brilliancy,  from  that  of 
the  brightest  to  those  which  are  barely  visible.  We  also 
notice  at  a  glance  that  the  fainter  stars  outnumber  the 
bright  ones;  so  that  if  we  divide  the  stars  into  classes  ac- 
cording to  their  brilliancy,  the  fainter  classes  will  contain 
the  most  stars. 

The  total  number  one  can  see  will  depend  very  largely 
upon  the  clearness  of  the  atmosphere  and  the  keenness  of 
the  eye.  There  are  in  the  whole  celestial  sphere  about 
6000  stars  visible  to  an  ordinarily  good  eye.  Of  these, 
however,  we  can  never  see  more  than  a  fraction  at  any 
one  time,  because  one  half  of  the  sphere  is  always  below  the 
horizon.  If  we  could  see  a  star  in  the  horizon  as  easily  as 
in  the  zenith,  one  half  of  the  whole  number,  or  3000,  would 
be  visible  on  any  clear  night.  But  stars  near  the  horizon 
are  seen  through  so  great  a  thickness  of  atmosphere  as 
greatly  to  obscure  their  light ;  consequently  only  the 


CONSTELLATIONS.  289 

brightest  ones  can  there  be  seen.  As  a  result  of  this  ob- 
scuration, it  is  not  likely  that  more  than  2000  stars  can 
ever  be  taken  in  at  a  single  yiew  by  any  ordinary  eye. 
About  2000  other  stars  are  so  near  the  south  pole 
that  they  never  rise  in  our  latitudes.  Hence  out  of  the 
6000  supposed  to  be  visible,  only  4000  ever  come  within 
the  range  of  our  vision,  unless  we  make  a  journey  toward 
the  equator. 

The  Galaxy. — Another  feature  of  the  heavens,  which  is 
less  striking  than  the  stars,  but  has  been  noticed  from 
the  earliest  times,  is  the  Galaxy,  or  Milky  Way.  This 
object  consists  of  a  magnificent  stream  or  belt  of  white 
milky  light  10°  or  15°  in  breadth,  extending  obliquely 
around  the  celestial  sphere.  During  the  spring  months  it 
nearly  coincides  with  our  horizon  in  the  early  evening, 
but  it  can  readily  be  seen  at  all  other  times  of  the  year 
spanning  the  heavens  like  an  arch.  It  is  for  a  portion  of 
its  length  split  longitudinally  into  two  parts,  which  remain 
separate  through  many  degrees,  and  are  finally  united 
again.  The  student  will  obtain  a  better  idea  of  it  by 
actual  examination  than  from  any  description.  He  will 
see  that  its  irregularities  of  form  and  lustre  are  such  that 
in  some  places  it  looks  like  a  mass  of  brilliant  clouds. 

Lucid  and  Telescopic  Stars. — When  we  view  the  heavens 
with  a  telescope,  we  find  that  there  are  innumerable  stars 
too  small  to  be  seen  by  the  naked  eye.  We  may  there- 
fore divide  the  stars,  with  respect  to  brightness,  into  two 
great  classes. 

Lucid  Stars  are  those  which  are  visible  without  a  tele- 
scope. 

Telescopic  Stars  are  those  which  are  not  so  visible. 

When  GALILEO  first  directed  his  telescope  to  the  heav- 


290  ASTRONOMY. 

ens,  about  the  year  1610,  he  perceived  that  the  Milky 
Way  was  composed  of  stars  too  faint  to  be  individually 
seen  by  the  unaided  eye.  We  thus  have  the  interesting 
fact  that  although  telescopic  stars  cannot  be  seen  one  by 
one,  yet  in  the  region  of  the  Milky  Way  they  are  so  numer- 
ous that  they  shine  in  masses  like  brilliant  clouds.  HUY- 
GHENS  in  1656  resolved  a  large  portion  of  the  Galaxy  into 
stars,  and  concluded  that  it  was  composed  entirely  of  them. 
KEPLEK  considered  it  to  be  a  vast  ring  of  stars  surround 
ing  the  solar  system,  and  remarked  that  the  sun  must  be 
situated  near  the  centre  of  the  ring.  This  view  ngrecs 
very  well  with  the  one  now  received,  only  that  the  stars 
which  form  the  Milky  Way,  instead  of  lying  around  the 
solar  system,  are  at  a  distance  so  vast  as  to  elude  all  our 
powers  of  calculation. 

Such  are  in  brief  the  more  salient  phenomena  which 
are  presented  to  an  observer  of  the  starry  heavens.  We 
shall  now  consider  how  these  phenomena  have  been  clas- 
sified by  an  arrangement  of  the  stars  according  to  their 
brilliancy  and  their  situation. 

MAGNITUDES  OF  THE  STARS. 

In  ancient  times  the  stars  were  arbitrarily  classified  into  six 
orders  of  magnitude.  The  fourteen  brightest  visible  in  our  lati- 
tude were  designated  as  of  the  first  magnitude,  while  those  which 
were  barely  visible  to  the  naked  eye  were  said  to  be  of  the  sixth 
magnitude.  This  classification,  it  will  be  noticed,  is  entirely  arbi- 
trary, since  there  are  no  two  stars  which  are  absolutely  of  the  same 
brightness;  that  is,  if  all  the  stars  were  arranged  in  the  order  of 
their  actual  brilliancy,  we  should  find  a  regular  gradation  from  the 
brightest  to  the  faintest,  no  two  being  precisely  the  same.  There- 
fore the  brightest  star  of  any  one  magnitude  is  about  of  the  same 
brilliancy  with  the  faintest  one  of  the  next  higher  magnitude.  Be- 
tween the  north  pole  and  35°  south  declination  there  are: 


CONSTELLATIONS.  291 

14  stars  of  the  first  magnitude.  - 

48    "        "      second    " 

152     "        "      third       " 

313     "        "      fourth    " 

854     "        "      fifth        " 

3974    "        "      sixth       " 

5355  of  the  first  six  magnitudes. 

Of  these,  however,  nearly  2000  of  the  sixth  magnitude  are  so  faint 
that  they  can  be  seen  only  by  an  eye  of  extraordinary  keenness.  A 
star  of  the  second  magnitude  is  four  tenths  as  bright  as  one  of  the 
first;  one  of  the  third  is  four  tenths  as  bright  as  one  of  the  second, 
and  so  on. 


THE  CONSTELLATIONS  AND  NAMES  OF  THE  STABS. 

The  earliest  astronomers  divided  the  stars  into  groups, 
called  constellations,  and  gave  special  proper  names  both 
to  these  groups  and  to  many  of  the  more  conspicuous 
stars. 

We  have  evidence  that  more  than  3000  years  before  the  commence- 
ment of  the  Christian  chronology  the  star  Sinus,  the  brightest  in  the 
heavens,  was  known  to  the  Egyptians  under  the  name  of  Sothis. 
The  seven  stars  of  the  Great  Bear,  so  conspicuous  in  our  northern 
sky,  were  known  under  that  name  to  HOMER  and  HESIOD,  as  well  as 
the  group  of  the  Pleiades,  or  Seven  Stars,  and  the  constellation  of 
Orion.  Indeed,  it  would  seem  that  all  the  earlier  civilized  nations, 
Egyptians,  Chinese,  Greeks,  and  Hindoos,  had  some  arbitrary  divi- 
sion of  the  surface  of  the  heavens  into  irregular  and  often  fantastic 
shapes,  which  were  distinguished  by  names. 

In  early  times  the  names  of  heroes  and  animals  were  given  to  the 
constellations,  and  these  designations  have  come  down  to  the  present 
day.  Each  object  was  supposed  to  be  painted  on  the  surface  of  the 
heavens,  and  the  stars  were  designated  by  their  position  upon  some 
portion  of  the  object.  The  ancient  and  mediaeval  astronomers  would 
speak  of  "the  bright  star  in  the  left  foot  of  Orion,"  "  the  eye  of  the 
Bull,"  "the  heart  of  the  Lion,"  "the  head  of  Perseus,"  etc.  These 
figures  are  still  retained  upon  some  star-charts,  and  are  useful  where 
it  is  desired  to  compare  the  older  descriptions  of  the  constellations 
with  our  modern  maps.  Otherwise  they  have  ceased  to  serve  any 


292  ASTRONOMY. 

purpose,  and  are  not  generally  found  on  maps  designed  for  purely 
astronomical  uses. 

The  Arabians,  who  used  this  clumsy  way  of  designating  stars, 
gave  special  names  to  a  large  number  of  the  brighter  ones.  Some  of 
these  names  are  iu  common  use  at  the  present  time,  as  Aldebaran, 
Fomalhaut,  etc. 

In  1654  BAYER,  of  Germany,  mapped  down  the  constellations 
upon  charts,  designating  the  brighter  stars  of  each  constellation  by 
the  letters  of  the  Greek  alphabet.  When  this  alphabet  was  exhaust- 
ed he  introduced  the  letters  of  the  Roman  alphabet.  In  general,  the 
brightest  star  was  designated  by  the  first  letter  of  the  alphabet,  a, 
the  next  by  the  following  letter,  ft,  etc. 

On  this  system,  a  star  is  designated  by  a  certain  Greek  letter,  fol- 
lowed by  the  genitive  of  the  Latin  name  of  the  constellation  to  which 
it  belongs.  For  example,  a  Canis  flfajoris,  or,  in  English,  a  of  the 
Great  Dog,  is  the  designation  of  Sinus,  the  brightest  star  in  the 
heavens.  The  seven  stars  of  the  Great  Bear  are  called  a  Ursa  Ma- 
joris,  ft  Ursce  Majorin,  etc.  Arcturus  is  a  Bootis.  The  reader  will 
here  see  a  resemblance  to  our  way  of  designating  individuals  by  a 
Christian  name  followed  by  the  family  name.  The  Greek  letters 
furnish  the  Christian  names  of  the  separate  stars,  while  the  name  of 
the  constellation  is  that  of  the  family.  As  there  are  only  fifty  letters 
in  the  two  alphabets  used  by  BAYER,  it  will  be  seen  that  only  the 
fifty  brightest  stars  in  each  constellation  could  be  designated  by  this 
method. 

When  by  the  aid  of  the  telescope  many  more  stars  than  these  were 
laid  down,  some  other  method  of  denoting  them  became  necessary. 
FLAMSTEED,  who  observed  before  and  after  1700,  prepared  an  ex- 
tensive catalogue  of  stars,  in  which  those  of  each  constellation  were 
designated  by  numbers  in  the  order  of  right  ascension.  These  num- 
bers were  entirely  independent  of  the  designations  of  BAYER — that 
is,  he  did  not  omit  the  BAYER  stars  from  his  system  of  numbers,  but 
numbered  them  as  if  they  had  no  Greek  letter.  Hence  those  stars  to 
which  BAYER  applied  letters  have  two  designations,  the  number  and 
the  letter.  The  fainter  stars  are  designated  either  by  their  R.A.  and 
d,  or  by  their  numbers  in  some  catalogue  of  stars. 

NUMBERING  AND  CATALOGUING  THE  STABS. 

As  telescopic  power  is  increased,  we  still  find  stars  of  fainter  and 
fainter  light.  But  the  number  cannot  go  on  increasing  forever  in 
the  same  ratio  as  with  the  brighter  magnitudes,  because,  if  it  did, 
the  whole  sky  would  be  a  blaze  of  starlight, 


CON  STELLA  TTON8. 


293 


If  telescopes  with  powers  far  exceeding  our  present  ones  were 
made,  they  would  no  doubt  show  new  stars  of  the  20th  and  21st 
magnitudes.  But  it  is  highly  probable  that  the  number  of  such  suc- 
cessive orders  of  stars  would  not  increase  in  the  same  ratio  as  is  ob- 
served in  the  8th,  9th,  and  10th  magnitudes,  for  example.  The 
enormous  labor  of  estimating  the  number  of  stars  of  such  classes  will 
long  prevent  the  accumulation  of  statistics  on  this  question ;  but  this 
much  is  certain,  that  in  special  regions  of  the  sky,  which  have  been 
searchingly  examined  by  various  telescopes  of  successively  increas- 
ing apertures,  the  number  of  new  stars  found  is  by  no  means  in  pro- 
portion to  the  increased  instrumental  power.  If  this  is  found  to  be 
true  elsewhere,  the  conclusion  may  be  that,  after  all,  the  stellar  sys- 
tem can  be  experimentally  shown  to  be  of  finite  extent,  or  to  con- 
tain only  a  finite  number  of  stars,  rather. 

We  have  already  stated  that  in  the  whole  sky  an  eye  of  average 
power  will  see  about  6000  stars.  With  a  telescope  this  number  is 
greatly  increased,  and  the  most  powerful  telescopes  of  modern  times 
will  probably  show  more  than  60,000,000  stars.  As  no  trustworthy 
estimate  has  ever  been  made,  there  is  great  uncertainty  upon  this 
point,  and  the  actual  number  may  range  anywhere  between 
40.000.000  to  100,000.000.  Of  this  number,  not  one  out  of  twenty 
has  ever  been  catalogued  at  all. 

The  southern  sky  has  many  more  stars  of  the  first  seven  magni- 
tudes than  the  northern,  and  the  zones  immediately  north  and  south 
of  the  equator,  although  greater  in  surface  than  any  others  of  the 
same  width  in  declination,  are  absolutely  poorer  in  such  stars. 

This  will  be  much  better  understood  by  consulting  the  grnphical 
representation  on  page  294.  On  this  chart  are  laid  down  all  the  stars 
of  the  British  Association  Catalogue  (a  dot  for  each  star),  and  beside 
these  the  Milky  Way  is  represented.  The  relative  richness  of  the 
various  zones  can  be  at  once  seen. 

The  distribution  and  number  of  the  brighter  stars  (1st  to  7th  magni- 
tude) can  be  well  understood  from  this  chart. 

In  ARGELANDER'S  Durchmuxterung  of  the  stars  of  the  northern 
heavens  there  are  recorded  as  belonging  to  the  northern  hemisphere: 


37 

128 

310 

1,016 

4,328 

13,593 

57,960 

237,544 


10  stars  between  the  1.0  magnitude  and  the  1.9  magnitude. 


2.0 
3.0 
4.0 
5.0 
6.0 
7.0 
8.0 
9.0 


2.9 
3.9 
4.9 
5.9 
6.9 
7.9 
8.9 
9.5 


294 


ASTRONOMY. 


CONSTELLATIONS. 


295 


In  all  314,926  stars  from  the  first  to  the  9.5  magnitudes  are  enu- 
merated in  the  northern  sky,  so  that  there  are  about  600,000  in  the 
whole  heavens. 

We  may  readily  compute  the  amount  of  light  received  by  the  earth 
on  a  clear  but  moonless  night  from  these  stars.  Let  us  assume  that 
the  brightness  of  an  average  star  of  the  first  magnitude  is  about  0.5 
of  that  of  a  LyroB.  A  star  of  the  2d  magnitude  will  shine  with  a 
light  expressed  by  0.5  X  0.4  =  0.20,  and  so  on.  (See  p.  291.) 

The  total  brightness  of 


10 
37 
128 
310 
1,016 
4,328 
13,593 
57,960 

1st  magi 
2d 
3d 
4th 
5th 
6th 
7th 
8th 

litude  st 

ars  is    5.0 
7.4 
102 
9.9 
13.0 
22.1 
27.8 
47.4 

Sum  =  142.8 

It  thus  appears  that  from  the  stars  to  the  8th  magnitude,  inclusive, 
we  receive  143  times  as  much  light  as  from  a  Lyres,  a  Lyres  has 
been  determined  by  ZOLLNER  to  be  about  44,000,000,000  times  fainter 
than  the  sun,  so  that  the  proportion  of  starlight  to  sunlight  can  be 
computed.  It  also  appears  that  the  stars  of  magnitudes  too  high  to 
allow  them  to  be  individually  visible  to  the  naked  eye  are  yet  so 
numerous  as  to  affect  the  general  brightness  of  the  sky  more  than 
the  so-called  lucid  stars  (1st  to  6th  magnitude).  The  sum  of  the  last 
two  numbers  of  the  table  is  greater  than  the  sum  of  all  the  others. 

NOTE. — At  the  end  of  this  book  two  Star  Maps  (with 
explanations)  are  given,  by  means  of  which  the  constella- 
tions and  principal  stars  can  be  identified.  The  larger 
map  is  copied  from  BRUHNS'  excellent  "Atlas  der  Astron- 
omic" (BROCKHAUS,  Leipzig,  1872). 


CHAPTER  II. 
VARIABLE  AND  TEMPORARY  STARS. 

STABS  REGULARLY  VAKIABLE. 

ALL  stars  do  not  shine  with  a  constant  light.  Since  the 
middle  of  the  seventeenth  century,  stars  variable  in  bril- 
liancy have  been  known.  The  period  of  a  variable  star 
means  the  interval  of  time  in  which  it  goes  through  all  its 
changes,  and  returns  to  its  original  brilliancy. 

The  most  noted  variable  stars  are  Mir  a  Ceti  (o  Ceti)  and 
Algol  (ft  Persei).  Mir  a  appears  about  twelve  times  in 
eleven  years,  and  remains  at  its  greatest  brightness  (some- 
times as  high  as  the  2d  magnitude,  sometimes  not  above 
the  4th)  for  some  time,  then  gradually  decreases  for  about 
74  days,  until  it  becomes  invisible  to  the  naked  eye,  and  so 
remains  for  about  five  or  six  months.  From  the  time  of 
its  reappearance  as  a  lucid  star  till  the  time  of  its  maximum 
is  about  43  days.  The  mean  period,  or  the  interval  from 
minimum  to  minimum,  is  about  333  days,  but  this  period 
varies  greatly.  The  brilliancy  of  the  star  at  the  maxima 
also  varies. 

Algol  has  been  known  as  a  variable  star  since  1667. 
This  star  is  commonly  of  the  2d  magnitude;  after  remain- 
ing so  about  2|  days,  it  falls  to  4m  in  the  short  time  of 
4|  hours,  and  remains  of  4ra  for  20  minutes.  It  then  com- 


VARIABLE  AND   TEMPORARY  STARS.  297 

mences  to  increase  in  brilliancy,  and  in  another  3$  hours  it 
is  again  of  the  2d  magnitude,  at  which  point  it  remains  for 
the  rest  of  its  period,  about  3d  12h. 

These  two  examples  of  the  class  of  variable  stars  give  a 
rough  idea  of  the  extraordinary  nature  of  the  phenomena 
they  present.  A  closer  examination  of  others  discloses 
minor  variations  of  great  complexity  and  apparently  with- 
out law. 

About  90  variable  stars  are  well  known,  and  as  many 
more  are  suspected  to  vary.  In  nearly  all  cases  the  mean 
period  can  be  fairly  well  determined,  though  anomalies  of 
various  kinds  frequently  appear.  The  principal  anomalies 
are: 

First.  The  period  is  seldom  constant.  For  some  stars 
the  changes  of  the  period  seem  to  follow  a  regular  law;  for 
others  no  law  can  be  fixed. 

Second.  The  time  from  a  minimum  to  the  next  maxi- 
mum is  usually  shorter  than  from  this  maximum  to  the 
next  minimum. 

Third.  Some  stars  (us  ft  Lyrce)  have  not  only  one  maxi- 
mum between  two  consecutive  principal  minima,  but  two 
such  maxima.  For  fi  Lyrce,  according  to  ARGELANDER, 
3d  2h  after  the  principal  minimum  comes  the  first  maxi- 
mum; then,  3d  7h  after  this,  a  secondary  minimum  in.which 
the  star  is  by  no  means  so  faint  as  in  the  principal  mini- 
mum, and  finally  3d  3h  afterward  comes  the  principal  maxi- 
mum, the  whole  period  being  12d  21h  47m. 

The  course  of  one  period  is  illustrated  in  the  following  table, 
supposing  the  period  to  begin  at  O4  Oh.  Opposite  each  phase  is 
given  the  intensity  of  light  in  terms  of  y  Lyr®  =  1. 


Phases  of  ft  Lyrae. 

Relative 
Intensity. 

Principal  Minimum  

0* 

O11 

040 

First  Maximum  

3d 

083 

Second  Minimum 

6d 

9h 

058 

Principal  Maximum 

9* 

12h 

089 

Principal  Minimum  

22m 

040 

The  periods  of  94  well-determined  variable  stars  being  tabulated, 
it  appears  that  they  are  as  follows: 


Period  between 

No.  of  Stars. 

Period 

between 

No.  of  Star* 

Id. 

and   20  d. 

13 

350  d.  ; 

ind  400  d. 

13 

20 

50 

1 

400 

450 

8 

50 

100 

4 

450 

500 

3 

100 

150 

4 

500 

550 

0 

150 

200 

5 

550 

600 

0 

200 

250 

9 

600 

650 

1 

250 

300 

14 

650 

700 

0 

300 

350 

18 

700 

750 

1 

2=94 

It  is  natural  that  there  should  be  few  known  variables  of  periods 
of  500  days  and  over,  but  it  is  not  a  little  remarkable  that  the  periods 
of  over  half  of  these  variables  should  fall  between  250  aud  450  days. 

The  color  of  over  80  per  cent  of  the  variable  stars  is  red  or  orange. 
Red  stars  (of  which  600  to  700  arc  known)  are  now  receiving  close 
attention,  as  there  is  a  strong  likelihood  of  finding  among  them  many 
new  variables. 

The  spectra  of  variable  stars  show  changes  which  appear  to  be 
connected  with  the  variations  in  their  light. 


TEMPORARY  OR  NEW  STARS. 

There  are  a  few  cases  known  of  apparently  new  stars  which  have 
suddenly  appeared,  attained  more  or  less  brightness,  and  slowly  de- 
creased in  magnitude,  either  disappearing  totally,  or  finally  remain- 
ing as  comparatively  faint  objects. 

The  most  famous  one  was  that  of  1572,  which  attained  a  brightness 


VARIABLE  AND  TEMPORARY  STARS. 


greater  than  that  of  Sirius  or  Jupiter  and  approached  to  Venus,  being 
even  visible  to  the  eye  in  daylight.  TYCHO  BRAHE  first  observed  this 
star  in  November,  1572,  and  watched  its  gradual  increase  in  light 
until  its  maximum  in  December.  It  then  began  to  diminish  in  bright- 
ness, and  in  January,  1573,  it  was  fainter  than  Jupiter.  In  February 
it  was  of  the  1st  magnitude,  in  April  of  the  2d,  in  July  of  the  3d,  and 
in  October  of  the  4th.  It  continued  to  diminish  until  March,  1574, 
when  it  became  invisible,  as  the  telescope  was  not  then  in  use.  Its 
color,  at  first  intense  white,  decreased  through  yellow  and  red. 
When  it  arrived  at  the  5th  magnitude  its  color  again  became  white, 
and  so  remained  till  its  disappearance.  TYCHO  measured  its  distance 
carefully  from  nine  stars  near  it,  and  near  its  place  there  is  now  a  star 
of  the  10th  or  llth  magnitude,  which  is  possibty  the  same  star. 

The  history  of  temporary  stars  is  in  general  similar  to  that  of  the 
star  of  1572,  except  that  none  have  attained  so  great  a  degree  of  bril- 
liancy. More  than  a  score  of  such  objects  are  known  to  have  ap- 
peared, many  of  them  before  the  making  of  accurate  observations, 
and  the  conclusion  is  probable  that  many  have  appeared  without 
recognition.  Among  telescopic  stars  there  is  but  a  small  chance  of 
detecting  a  new  or  temporary  star. 

Several  supposed  cases  of  the  disappearance  of  stars  exist,  but  here 
there  are  so  many  possible  sources  of  error  that  great  caution  is  neces- 
sary in  admitting  them. 

Two  temporary  stars  have  appeared  since  the  invention  of  the  spec- 
troscope (1859),  and  the  conclusions  drawn  from  a  study  of  their  spec- 
tra are  most  important  as  throwing  light  upon  the  phenomena  of 
variable  stars  in  general. 

The  general  theory  of  variable  stars  which  has  now  the  most  evi- 
dence in  its  favor  is  this:  These  bodies  are,  from  some  general  cause 
not  fully  understood,  subject  to  eruptions  of  glowing  hydrogen  gas 
from  their  interior,  and  to  the  formation  of  dark  spots  on  their  sur- 
faces. These  eruptions  and  formations  have  in  most  cases  a  greater 
or  less  tendency  to  a  regular  period. 

In  the  case  of  our  sun  (which  is  a  variable  star)  the  period  is  11 
years,  but  in  the  case  of  many  of  the  stars  it  is  much  shorter.  Ordi- 
narily, as  in  the  case  of  the  sun  and  of  a  large  majority  of  the  stars, 
the  variations  are  too  slight  to  affect  the  total  quantity  of  light  to  any 
visible  extent.  But  in  the  case  of  the  variable  stars  this  spot-producing 
power  and  the  liability  to  eruptions  are  very  much  greater,  and  thus 
we  have  changes  of  light  which  can  be  readily  perceived  by  the  eye. 
Some  additional  strength  is  given  to  this  theory  by  the  fact  just  men- 
tioned, that  so  large  a  proportion  of  the  variable  stars  are  red.  It  is  well 
known  that  glowing  bodies  emit  a  larger  proportion  of  red  rays  and 


300  ASTRONOMY. 

a  smaller  proportion  of  blue  ones  the  cooler  they  become.  It  is  there- 
fore probable  that  the  red  stars  have  the  least  heat.  This  being  the 
case,  it  is  more  easy  to  produce  spots  on  their  surface;  and  if  their 
outside  surface  is  so  cool  as  to  become  solid,  the  glowing  hydrogen 
from  the  interior  when  it  did  burst  through  would  do  so  with  more 
power  than  if  the  surrounding  shell  were  liquid  or  gaseous.  » 

There  is,  however,  at  least  one  star  of  which  the  variations  may  be 
due  to  an  entirely  different  cause;  namely,  Algol.  The  extreme  regu- 
larity with  which  the  light  of  this  object  fades  away  and  disappears 
suggest*  the  possibility  that  a  dark  body  may  be  revolving  around  it, 
and  partially  eclipsing  it  at  every  revolution.  The  law  of  variation 
of  its  light  is  so  different  from  that  of  the  light  of  other  variable  stars 
as  to  suggest  a  different  cause.  Most  others  are  near  their  maximum 
for  only  a  small  part  of  their  period,  while  Algol  is  at  its  maximum 
for  nine  tenths  of  it.  Others  are  subject  to  nearly  continuous  changes, 
while  the  light  of  Algol  remains  constant  during  nine  tenths  of  its 
period. 


CHAPTER  III. 
MULTIPLE    STARS. 

CHAEACTEE  OF  DOUBLE  AND  MULTIPLE  STAES. 


we  examine  the  heavens  with  telescopes,  we  find 
many  cases  in  which  two  or  more  stars  are  extremely  close 
together,  so  as  to  form  a  pair,  a  triplet,  or  a  group.  It  is 
evident  that  there  are  two  ways  to  account  for  this  appear- 
ance. 

1.  We  may  suppose  that  the  stars  happen  to  lie  nearly 
in  the  same  straight  line  from  us,  but  have  no  connection 
with  each  other.     It  is  evident  that  in  this  case  a  pair  of 
stars  might  appear  double,  although  the  one  was  hundreds 
or  thousands  of  times  farther  off  than  the  other.     It  is, 
moreover,  impossible,  from  mere  inspection,  to  determine 
which  is  the  farther  off. 

2.  We  may  suppose  that  the  stars  are  really  near  together, 
as  they  appear,  and  are  to  be  considered  as  forming  a  con- 
nected pair  or  group. 

A  couple  of  stars  in  the  first  case  is  said  to  be  optically 
double. 

Stars  which  are  really  physically  connected  are  said  to  be 
physically  double. 

If  the  lucid  stars  are  equally  distributed  over  the  celestial  sphere, 
the  chances  are  80  to  1  against  any  two  being  within  three  minutes 
of  each  other,  and  the  chances  are  500,000  to  1  against  the  six  visible 
stars  of  the  Pleiades  being  accidentally  associated  as  we  see  them. 
When  the  millions  of  telescopic  stars  are  considered,  there  is  a  greater 


302  ASTSONOMY. 

i 

probability  of  such  accidental  juxtaposition.  But  the  probability  of 
many  such  cases  occurring  is  so  extremely  small  that  astronomers 
regard  all  the  closest  pairs  as  physically  connected.  Of  the  600,000 
stars  of  the  first  ten  magnitudes,  about  10,000,  or  one  out  of  every 
60,  has  a  companion  within  a  distance  of  30"  of  arc.  This  proportion 

is  many  times  greater  than  could  possi- 
bly be  the  result  of  chance  distribution. 
There  are  several  cases  of  stars  which 
appear  double  to  the  naked  eye.    e  Lyra 
is  such  a  star  and  is  an  interesting  ob- 
ject, from  the  fact  that  each  of  the  two 
stars  which  compose  it  is  itself  double. 
This  minute  pair  of  points,  capable  of 
being  distinguished  as  double  only  by 
the  most  perfect  eye  (without  the  tele- 
scope), is  really  composed  of  two  pairs 
Fio.  86.— THK  QrADRtjpLK  STAR  of   stars  wide  apart,  with  a  group  of 
«  LYR*L  smaller    stars    between     and     around 

them.  The  figure  shows  the  appearance  in  a  telescope  of  consider- 
able power. 

Bevolutions  of  Double  Stars— Binary  Systems. — It  is  evident  that  if 
double  stars  are  endowed  with  the  property  of  mutual  gravitation, 
they  must  be  revolving  around 
each  other,  as  the  earth  and 
planets  revolve  around  the  sun, 
else  they  would  be  'drawn  to- 
gether as  a  single  star. 

The  method  of  determining 
the  period  of  revolution  of  a 
binary  star  is  illustrated  by  the 
figure,  which  is  supposed  to  rep- 
resent the  field  of  view  of  an  in- 
verting telescope  pointed  toward 
the  south.  The  arrow  shows  the 
direction  of  the  apparent  diur- 
nal motion.  The  telescope  is 
supposed  to  be  so  pointed  that 
the  brighter  star  may  be  in  the 
centre  of  the  field.  The  num- 
bers around  the  surrounding  Flo>  87-~" POSITIOKKA^QLE  OP  A  DOUBLE 
circle  then  show  the  angle  of 

position,  supposing  the  smaller  star  to  be  in  the  direction  of  the 
number. 


MULTIPLE  STARS.  303 

Fig.  87  is  a  a  example  of  a  pair  of  stars  in  which  the  position- 
angle  is  about  44°. 

If,  by  measures  of  this  sort  extending  through  a  series  of  years,  the 
distance  or  position-angle  of  a  pair  of  stars  is  found  to  change  peri- 
odically, it  shows  that  one  star  is  revolving  around  the  other.  Such 
a  pair  is  called  a  binary  star  or  binary  system.  The  only  distinction 
which  we  can  make  between  binary  systems  and  ordinary  double 
stars  is  founded  on  the  presence  or  absence  of  this  observed  motion. 
It  is  probable  that  nearly  all  the  very  close  double  stars  are  really 
binary  systems,  but  that  many  hundreds  of  years  are  required  to  per- 
form a  revolution  in  some  instances,  so  that  the  motion  has  not  yet 
been  detected. 

The  discovery  of  binary  systems  is  one  of  great  scientific  interest, 
because  from  them  we  learn  that  the  law  of  gravitation  includes  the 
stars  as  well  as  the  solar  system  in  its  scope,  and  may  thus  be  regarded 
as  truly  universal. 

When  the  parallax  of  a  binary  star  is  known,  as  well  as  the  orbit, 
it  is  possible  to  compute  the  mass  of  the  binary  system  in  terms  of 
the  sun's  mass.  It  is  an  important  fact  that  such  binary  systems  as 
have  been  investigated  do  not  differ  greatly  in  mass  from  our  sun. 


CHAPTER  IV. 
NEBULA  AND  CLUSTERS. 

DISCOVERY  OF  NEBTJLE. 

IN  the  star-catalogues  of  PTOLEMY,  HEVELIUS,  and  the 
earlier  writers,  there  was  included  a  class  of  nebulous  or 
cloudy  stars,  which  were  in  reality  star-clusters.  They  ap- 
peared to  the  naked  eye  as  masses  of  soft  diffused  light  of 
greater  or  less  extent.  In  this  respect  they  were  quite 
analogous  to  the  Milky  Way.  In  the  telescope,  the  nebu- 
lous appearance  of  these  spots  vanishes,  and  they  are  seen 
to  consist  of  clusters  of  stars. 

As  the  telescope  was  improved,  great  numbers  of  such 
patches  of  light  were  found,  some  of  which  could  be  re- 
solved into  stars,  while  others  could  not.  The  latter  were 
called  nebuldB  and  the  former  star-clusters. 

About  1656  HUYGHENS  described  the  great  nebula  of 
Orion,  one  of  the  most  remarkable  and  brilliant  of  these 
objects.  During  the  last  century  MESSIER,  of  Paris,  made 
a  list  of  103  northern  nebulae,  and  LACAILLE  noted  a  few 
of  those  of  the  southern  sky.  Sir  WILLIAM  HERSCHEL 
with  his  great  telescopes  first  gave  proof  of  the  enormous 
number  of  these  masses.  In  1 786  he  published  a,  catalogue 
of  one  thousand  new  nebulae  and  clusters.  This  was  fol- 
lowed in  1789  by  a  catalogue  of  a  second  thousand,  and  in 
1802  by  a  third  catalogue  of  five  hundred  new  objects  of 
this  class.  Sir  JOHN  HERSCHEL  added  about  two  thou- 


NEBULA  AND   CLUSTERS.  305 

sand  more  nebulae.  The  general  catalogue  of  nebulae  and 
clusters  of  stars  of  the  latter  astronomer,  published  in 
1864,  contains  5079  nebulae.  Over  two  thirds  of  these 
were  first  discovered  by  the  HERSCHELS. 

CLASSIFICATION  OF  NEBULA  AND  CLUSTEBS. 

In  studying  these  objects,  the  first  question  we  meet  is  this:  Are 
all  these  bodies  clusters  of  stars  which  look  diffused  only  because 
they  are  so  distant  that  our  telescopes  cannot  distinguish  them  sepa- 
rately? or  are  some  of  them  in  reality  what  they  seem  to  be;  namely, 
diffused  masses  of  matter? 

In  his  early  memoirs  of  1784  and  1785,  Sir  WILLIAM  HEKSCHEL 
took  the  first  view.  He  considered  the  Milky  Way  as  nothing  but  a 
congeries  of  stars,  and  all  nebulae  naturally  seemed  1o  him  to  be  but 
stellar  clusters,  so  distant  as  to  cause  the  individual  stars  to  disap- 
pear in  a  general  milkiness  or  nebulosity. 

In  1791,  however,  his  views  underwent  a  change.  He  had  dis- 
covered a  nebulous  star  (properly  so  called),  or  a  star  which  was  un- 
doubtedly similar  to  the  surrounding  stars,  and  which  was  encom- 
passed by  a  halo  of  nebulous  light. 

He  says:  "Nebulae  can  be  selected  so  that  an  insensible  gradation 
shall  take  place  from  a  coarse  cluster  like  the  Pleiades  down  to  a 
milky  nebulosity  like  that  in  Orion,  every  intermediate  step  being 
represented.  This  tends  to  confirm  the  hypothesis  that  all  are  com- 
posed of  stars  more  or  less  remote. 

"  A  comparison  of  the  two  extremes  of  the  series,  as  a  coarse  cluster 
and  a  nebulous  star,  indicates,  however,  that  the  nebulosity  about  the 
star  is  not  of  a  starry  nature. 

"Considering  a  typical  nebulous  star,  and  supposing  the  nucleus 
and  chevelure  to  be  connected,  we  may,  first,  suppose  the  whole 
to  be  of  stars,  in  which  case  either  the  nucleus  is  enormously 
larger  than  other  stars  of  its  stellar  magnitude,  or  the  envelope  is 
composed  of  stars  indefinitely  small;  or,  second,  we  must  admit  that 
the  star  is  involved  in  a  shining  fluid  of  a  nature  totally  unknown  to 
us. 

"The  shining  fluid  might  exist  independently  of  stars.  The 
light  of  this  fluid  is  no  kind  of  reflection  from  the  star  in  the 
centre.  If  this  matter  is  self-luminous,  it  seems  more  fit  to  pro- 
duce a  star  by  its  condensation  than  to  depend  on  the  star  for  its 
existence. 


306 


ASTRONOMY. 


"Both  diffused  nebulosities  and  planetary  nebulae  are  better  ac- 
counted for  by  the  hypothesis  of  a  shining  fluid  than  by  supposing 
them  to  be  distant  stars." 

This  was  the  first  exact  statement  of  the  idea  that,  beside  stars 
and  star-clusters,  we  have  in  the  universe  a  totally  distinct  series  of 
objects,  probably  much  more  simple  in  their  constitution.  Observa- 
tions on  the  spectra  of  these  bodies  have  entirely  confirmed  the  con- 
clusions of  HERSCIIEL. 

Nebulae  and  clusters  were  divided  by  HERSCHEL  into  classes.    He 


FIG.  88.— SPIRAL  NEBULA. 

applied  the  name  planetary  nebulae,  to  certain  circular  or  elliptic 
nebulae  which  in  his  telescope  presented  disks  like  the  planets. 
Spiral  nebula  are  those  whose  convolutions  have  a  spiral  shape.  This 
class  is  quite  numerous. 

The  different  kinds  of  nebulae  and  clusters  will  be  better  under- 
stood from  the  cuts  and  descriptions  which  follow  than  by  formal 
definitions.  It  must  be  remembered  that  there  is  an  almost  infinite 
variety  of  such  shapes. 


NEBULAE  AND  CLUSTERS. 


307 


FIG.  89.— THE  OMEGA  OR  HORSESHOK 


308 


ASTRONOMY. 


STAB-CLTTSTEBS. 

The  most  noted  of  all  the  clusters  is  the  Pleiades,  which  may  be 
seen  during  the  winter  months  to  the  northwest  of  the  constellation 
Taurus.  The  average  naked  eye  can  easily  distinguish  six  stars 
within  it,  but  under  favorable  conditions  ten,  eleven,  twelve,  or  more 
stars  can  be  counted.  With  the  telescope,  over  a  hundred  stars  are 
seen. 

The  clusters  represented  in  Figs.  90  and  91  are  good  examples  of 
their  classes.  The  first  is  globular  and  contains  several  thousand 
small  stars.  The  second  is  a  cluster  of  about  200  stars,  of  magni- 
tudes varying  from  the  ninth  to  the  thirteenth  and  fourteenth,  in 
which  the  brighter  stars  are  scattered. 


Fia.  90— GLOBULAR  CLUSTER. 


FIG.  01  —COMPRESSED  CLUSTER. 


Clusters  are  probably  subject  to  central  powers  or  forces.  This  was 
seen  by  Sir  WILLIAM  HERSCHEL  in  1789.  He  says : 

"Not  only  were  round  nebulae  and  clusters  formed  by  central 
powers,  but  likewise  every  cluster  of  stars  or  nebula  that  shows  a 
gradual  condensation  or  increasing  brightness  toward  a  centre. 
This  theory  of  central  power  is  fully  established  on  grounds  of  ob- 
servation which  cannot  be  overturned. 

"Clusters  can  be  found  of  10'diameter  with  a  certain  degree  of 
compression  and  stars  of  a  certain  magnitude,  and  smaller  clusters 
of  4',  3',  or  2'  in  diameter,  with  smaller  stars  and  greater  compression, 
and  so  on  through  resolvable  nebulas  by  imperceptible  steps,  to  the 


NEBULAE  AND  CLUSTERS.  309 

smallest  and  faintest  [and  most  distant]  nebulae.  Other  clusters  there 
are,  which  lead  to  the  belief  that  either  they  are  more  compressed  or 
are  composed  of  larger  stars.  Spherical  clusters  are  probably  not 
more  different  in  size  among  themselves  than  different  individuals  of 
plants  of  the  same  species.  As  it  has  been  shown  that  the  spherical 
figure  of  a  cluster  of  stars  is  owing  to  central  powers,  it  follows  that 
those  clusters  which,  cceterit  paribus,  are  the  most  complete  in  this 
figure  must  have  been  the  longest  exposed  to  the  action  of  these 
causes. 

"The  maturity  of  a  sidereal  system  may  thus  be  judged  from  the 
disposition  of  the  component  parts. 

"  Though  we  cannot  see  any  individual  nebula  pass  through  all 
its  stages  of  life,  we  can  select  particular  ones  in  each  peculiar 
stage,"  and  thus  obtain  a  single  view  of  their  entire  course  of  de- 
velopment. 

SPECTRA  OF  NEBUUE  AND  CLUSTERS,  AND  FIXED  STARS, 

In  1864,  five  years  after  the  invention  of  the  spectroscope,  the 
examination  of  the  spectra  of  the  nebulae  led  to  the  discovery  that 
while  the  spectra  of  stars  were  invariably  continuous  and  crossed  with 
dark  lines  similar  to  those  of  the  solar  spectrum,  those  of  many  ne- 
bulae were  discontinuous,  showing  these  bodies  to  be  composed  of 
glowing  gas. 

The  spectrum  of  most  clusters  is  continuous,  indicating  that  the 
individual  stars  are  truly  stellar  in  their  nature.  In  a  few  cases, 
however,  clusters  are  composed  of  a  mixture  of  nebulosity  (usually 
near  their  centre)  and  of  stars,  and  the  spectrum  in  such  cases  is 
compound  in  its  nature,  so  as  to  indicate  radiation  both  by  gaseous 
and  solid  matter. 

SPECTRA  OF  FIXED  STARS. 

Stellar  spectra  are  found  to  be,  in  the  main,  similar  to  the  solar 
spectrum;  i.e.,  composed  of  a  continuous  band  of  the  prismatic  col- 
ors, across  which  dark  lines  or  bands  were  laid,  the  latter  being  fixed 
in  position.  These  results  show  the  fixed  stars  to  resemble  our  own 
sun  in  general  constitution,  and  to  be  composed  of  an  incandescent 
nucleus  surrounded  by  a  gaseous  and  absorptive  atmosphere  of 
lower  temperature.  This  atmosphere  around  many  stars  is  different 
in  constitution  from  that  of  the  sun,  as  is  shown  by  the  different  posi- 
tion and  intensity  of  the  various  black  lines  and  bands  which  are  due 
to  the  absorptive  action  of  th,e  atmospheres  of  the  stars, 


310  ASTRONOMY. 

It  is  probable  that  the  hotter  a  star  is  the  more  simple  a  spectrum 
it  has;  for  the  brightest,  and  therefore  probably  the  hottest  stars, 
such  as  Sirius,  give  spectra  showing  only  very  thick  hydrogen  lines 
and  a  few  very  thin  metallic  lines,  while  the  cooler  stars,  such  as 
our  sun,  are  shown  by  their  spectra  to  contain  ;i  much  larger  num- 
ber of  metallic  elements  than  stars  of  the  type  of  Sinus,  but  no 
non-metallic  elements  (oxygen  possibly  exccptcd).  The  coolest 
stars  give  band  spectra  characteristic  of  compounds  of  metallic 
with  non-metallic  elements,  and  of  the  non  metallic  elements  uu- 
combined. 

MOTION  OF  STARS  IN  THE  LINE  OF  SIGHT. 

Spectroscopic  observations  of  stars  not  only  give  information  in 
regard  to  their  chemical  and  physical  constitution,  but  have  been 
applied  so  as  to  determine  approximately  the  velocity  in  kilometres 
per  second  with  which  the  stars  are  approaching  to  or  receding  from 
the  earth  along  the  line  joining  earth  and  star.  The  theory  of  such  a 
determination  is  briefly  as  follows: 

In  the  solar  spectrum  we  find  a  group  of  dark  lines,  as  a,  b,  c, 
which  always  maintain  their  relative  position.  From  laboratory 
experiments,  we  can  show  that  the  three  bright  lines  of  incandescent 
hydrogen  (for  example)  have  always  the  same  relative  position  as 
the  solar  dark  lines  a,  b,  c.  From  this  it  is  inferred  that  the  solar 
dark  lines  are  due  to  the  presence  of  hydrogen  in  its  absorptive 
atmosphere. 

Now,  suppose  that  in  a  stellar  spectrum  we  find  three  dark  lines 
a',  b',  c'.  whose  relative  position  is  exactly  the  same  as  that  of  the 
solar  lines  a,  b,  c.  Not  only  is  their  relative  position  the  same,  but 
the  characters  of  the  lines  themselves,  so  far  as  the  fainter  spectrum 
of  the  star  will  allow  us  to  determine  them,  are  also  similar;  that  is, 
a'  and  «,  b'  and  b,  c'  and  c  are  alike  as  to  thickness,  blackness,  nebu- 
losity of  edges,  etc.  etc.  From  this  it  is  inferred  that  the  star  really 
contains  in  its  atmosphere  the  substance  whose  existence  has  been 
shown  in  the  sun. 

If  we  contrive  an  apparatus  by  which  the  stellar  spectrum  is  seen 
in  the  lower  half,  say,  of  the  eye-piece  of  the  spectroscope,  while 
the  spectrum  of  hydrogen  is  seen  just  ab<-ve  it,  we  find  in  some 
cases  this  remarkable  phenomenon.  The  three  dark  stellar  lines, 
a',  bf,  c',  instead  of  being  exactly  coincident  with  the  three  hydrogen 
lines  a,  b,  c,  are  seen  to  be  all  thrown  to  one  side  or  the  other  by  a 
like  amount;  that  is,  the  whole  group  a',  b1 ',  c' ,  while  preserving  its 
relative  distances  the  same  as  those  of  the  comparison  group  a,  b  c, 


NEBULA  AND  CLUSTERS. 


311 


is  shifted  toward  either  the  violet  or  red  end  of  the  spectrum  by  a 
small  yet  measurable  amount.  Repeated  experiments  by  different 
instruments  and  observers  show  always  a  shifting  in  the  same  direc- 
tion and  of  like  amount.  The  figure  shows  the  shifting  of  the  P 
line  in  the  spectrum  of  Sirius,  compared  with  one  fixed  line  of 
hydrogen. 

This  displacement  of  the 
spectral  lines  is  to  be  ac- 
counted for  by  a  motion  of 
the  star  toward  or  from  the 
earth.  It  is  shown  in  Phy- 
sics that  if  the  source  of 
the  light  which  gives  the 
spectrum  a,  b',  c'  is  mov- 
ing away  from  the  earth, 
this  group  will  be  shifted 
toward  the  red  end  of  the 
spectrum ;  if  toward  the 
earth,  then  the  whole  group 
will  be  shifted  toward  the 
blue  end.  The  amount  of 
this  shifting  is  a  function  of 
the  velocity  of  recession  or 
approach,  and  this  velocity 
in  miles  per  second  can  be  calculated  from  the  measured  displace- 
ment. This  has  been  done  for  many  stars.  The  results  agree  well, 
when  the  difficult  nature  of  the  research  is  considered.  The  rates  of 
motion  vary  from  insensible  amounts  to  100  kilometres  per  second; 
and  in  some  cases  agree  remarkably  with  the  velocities  computed 
from  the  proper  motions  and  probable  parallaxes. 


FIG.  92.— F  LINE  IN  SPECTRUM  OP  SIRIUS. 


CHAPTER  V. 
MOTIONS   AND  DISTANCES   OF   THE   STARS. 

PROPER  MOTIONS. 

WE  have  already  stated  that,  to  the  unaided  vision,  the 
fixed  stars  appear  to  preserve  the  same  relative  position  in 
the  heavens  through  many  centuries,  so  that  if  the  an- 
cient astronomers  could  again  see  them,  they  could  hardly 
detect  the  slightest  change  in  their  arningement.  But 
accurate  measurements  have  shown  that  there  are  slow 
changes  in  the  positions  of  the  brighter  stars,  consisting  in 
a  motion  forward  in  a  straight  line  and  with  uniform 
velocity.  These  motions  are,  for  the  most  part,  so  slow 
that  it  would  require  thousands  of  years  for  the  change  of 
position  to  be  perceptible  to  the  unaided  eye.  They  are 
called  proper  motions,  since  they  are  peculiar  to  the  star 
itself. 

In  general,  the  proper  motions  even  of  the  brightest 
stars  are  only  a  fraction  of  a  second  in  a  year,  so  that 
thousands  of  years  would  be  required  for  them  to 
change  their  place  in  any  striking  degree,  and  hundreds 
of  thousands  to  make  a  complete  revolution  around  the 
heavens. 

PROPER  MOTION  OF  THE  SUN. 

It  is  a  priori  evident  that  stars,  in  general,  must  have 
proper  motions,  when  once  we  admit  the  universality  of 


MOTIONS  AND  DISTANCES  OF  THE  STARS.      313 

gravitation.  That  any  fixed  star  should  be  entirely  at 
rest  would  require  that  the  attractions  on  all  sides  of  it 
should  be  exactly  balanced.  Any  change  in  the  position 
of  this  star  would  break  up  this  balance,  and  thus,  in  gen- 
eral, it  follows  that  stars  must  be  in  motion,  since  all  of 
them  cannot  occupy  such  a  critical  position  as  has  to  be 
assumed. 

If  but  one  fixed  star  is  in  motion,  this  affects  all  the 
rest,  and  we  cannot  doubt  but  that  every  star,  our  sun 
included,  is  in  motion  by  amounts  which  vary  from  small 
to  great.  If  the  sun  alone  had  a  motion,  and  the  other 
stars  were  at  rest,  the  consequence  of  this  would  be  that 
all  the  fixed  stars  would  appear  to  be  retreating  en  masse 
from  that  point  in  the  sky  toward  which  we  were  moving. 
Those  nearest  us  would  move  more  rapidly,  those  more 
distant  less  so.  And  in  the  same  way,  the  stars  from 
which  the  solar  system  was  receding  would  seem  to  be 
approaching  each  other.  If  the  stars,  instead  of  being 
quite  at  rest,  as  just  supposed,  had  motions  proper  to 
themselves,  then  we  should  have  a  double  complexity. 
They  would  still  appear  to  an  observer  in  the  solar  system 
to  have  motions.  One  part  of  these  motions  would  be 
truly  proper  to  the  stars,  and  one  part  would  be  due  to  the 
advance  of  the  sun  itself  in  space. 

Observations  can  show  us  only  the  resultant  of  these 
two  motions.  It  is  for  reasoning  to  separate  this  resultant 
into  its  two  components.  At  first  the  question  is  to  deter- 
mine whether  the  results  of  observation  indicate  any  solar 
motion  at  all.  If  there  is  none,  the  proper  motions  of 
stars  will  be  directed  along  all  possible  lines.  If  the  sun 
does  truly  move,  then  there  will  be  a  general  agreement  in 
the  resultant  motions  of  the  stars  near  the  ends  of  the  line 


314  ASTRONOMY. 

along  which  it  moves,  while  those  at  the  sides,  so  to  speak, 
will  show  comparatively  less  systematic  effect.  It  is  as  if 
one  were  riding  in  the  rear  of  a  railway  train  and  watching 
the  rails  over  which  it  has  just  passed.  As  we  recede  from 
any  point,  the  rails  at  that  point  seem  to  come  nearer  and 
nearer  together. 

If  we  were  passing  through  a  forest,  we  should  see  the 
trunks  of  the  trees  from  which  we  were  going  apparently 
come  nearer  and  nearer  together,  while  those  on  the  sides 
of  us  would  remain  at  their  constant  distance,  and  those  in 
front  would  grow  further  and  further  apart. 

These  phenomena,  which  occur  in  a  case  where  we  are 
sensible  of  our  own  motion,  serve  to  show  how  we  may 
deduce  a  motion,  otherwise  unknown,  from  the  appear- 
ances which  are  presented  by  the  stars  in  space. 

In  this  way,  acting  upon  suggestions  which  had  been 
thrown  out  previously  to  his  own  time,  HERSCHEL  demon- 
started  that  the  sun,  together  with  all  its  system,  was  mov- 
ing through  space  in  an  unknown  and  majestic  orbit  of  its 
own.  The  centre  round  which  this  motion  is  directed 
cannot  yet  be  assigned.  We  can  only  determine  the  point 
in  the  heavens  toward  which  our  course  is  directed — "  the 
apex  of  solar  motion." 

A  number  of  astronomers  have  since  investigated  this 
motion  with  a  view  of  determining  the  exact  point  in  the 
heavens  toward  which  the  sun  is  moving.  Their  results 
differ  slightly,  but  the  points  toward  which  the  sun  is 
moving  all  fall  in  the  constellation  Hercules.  The  amount 
of  the  motion  is  such  that  if  the  sun  were  viewed  at  right 
angles  to  the  direction  of  motion  from  an  average  star 
of  the  first  magnitude,  it  would  appear  to  move  about  one 
third  of  a  second  per  year. 


MOTIONS  AND  DISTANCES  OF  T. 


DISTANCES  OF  THE  FIXED  STARS. 


The  ancient  astronomers  supposed  all  the  fixed  stars  to 
be  situated  at  a  short  distance  outside  of  the  orbit  of  the 
planet  Saturn,  then  the  outermost  known  planet.  The 
idea  was  prevalent  that  Nature  would  not  waste  space  by 
leaving  a  great  region  beyond  Saturn  entirely  empty. 

When  COPERKICUS  announced  the  theory  that  the  sun 
was  at  rest  and  the  earth  in  motion  around  it,  the  problem 
of  the  distance  of  the  stars  acquired  a  new  interest.  It  was 
evident  that  if  the  earth  described  an  annual  orbit,  then 
the  stars  would  appear  in  the  course  of  a  year  to  oscillate 
back  and  forth  in' Corresponding  orbits,  unless  they  were 
so  immensely  distant  that  these  oscillations  were  too  small 
to  be  seen.  The  apparent  oscillation  of  Saturn  pro- 
duced in  this  way  was  described  in  Part  I.  It  amounts  to 
some  6°  on  each  side  of  the  mean  position.  These  oscilla- 
tions were,  in  fact,  those  which  the  ancients  represented 
by  the  motion  of  the  planet  around  a  small  epicycle.  But 
no  such  oscillation  had  ever  been  detected  in  a  fixed  star. 
This  fact  seemed  to  present  an  almost  insuperable  difficulty 
in  the  reception  of  the  Copernican  system.  Very  natural- 
ly, therefore,  as  the  instruments  of  observation  were  from 
time  to  time  improved,  this  apparent  annual  oscillation  of 
the  stars  was  ardently  sought  for. 

The  problem  is  identical  with  that  of  the  annual  parallax 
of  the  fixed  stars,  which  has  been  already  described.  This 
parallax  of  a  heavenly  body  is  the  angle  which  the  mean 
distance  of  the  earth  from  the  sun  subtends  when  seen 
from  the  body.  The  distance  of  the  body  from  the  sun  is 
inversely  as  the  parallax  (nearly).  Thus  the  mean  distance 
of  Saturn  being  9.5,  its  annual  parallax  exceeds  6°,  while 


316  ASTliONOMY. 

that  of  Neptune,  which  is  three  times  as  far,  is  about  2°. 
It  was  very  evident,  without  telescopic  observation,  that 
the  stars  could  not  have  a  parallax  of  one  half  a  degree. 
They  must  therefore  be  at  least  twelve  times  as  far  as 
Saturn  if  the  Copernican  system  were  true. 

When  the  telescope  was  applied  to  measurement,  a  con- 
tinually increasing  accuracy  began  to  be  gained  by  the 
improvement  of  the  instruments.  Yet  for  several  genera- 
tions the  parallax  of  the  fixed  stars  eluded  measurement. 
Very  often  indeed  did  observers  think  they  had  detected 
a  parallax  in  some  of  the  brighter  stars,  but  their  succes- 
sors, on  repeating  their  measures  with  better  instruments, 
and  investigating  their  methods  anew,  found  their  conclu- 
sions erroneous.  Early  in  the  present  century  it  became 
certain  that  even  the  brighter  stars  had  not,  in  general,  a 
parallax  as  great  as  1*,  and  thus  it  became  certain  that  they 
must  lie  at  a  greater  distance  than  200,000  times  that 
which  separates  the  earth  from  the  sun. 

Success  in  actually  measuring  the  parallax  of  the  stars 
was  at  length  obtained  almost  simultaneously  by  two  as- 
tronomers, BESSEL  of  Konigsberg  and  STRUVE  of  Dorpat. 
BESSEL  selected  61  Gygni  for  observation,  in  August,  1837. 
The  result  of  two  or  three  years  of  observation  was  that 
this  star  had  a  parallax  of  0*.35,  or  about  one  third  of  a 
second.  This  would  make  its  distance  from  the  sun  nearly 
600,000  astronomical  units.  The  reality  of  this  parallax 
has  been  well-established  by  subsequent  investigators,  only 
it  has  been  shown  to  be  a  little  larger,  and  therefore  the 
star  a  little  nearer  than  BESSEL  supposed.  The  most  prob- 
able parallax  is  now  found  to  be  0" .  51,  corresponding  to  a 
distance  of  400,000  radii  of  the  earth's  orbit. 

The  distances  of  the  stars  arc  sometimes  expressed  by 


MOTIONS  AND  DISTANCES  OF  THE  STARS.      317 


the  time  required  for  light  to  pass  from  them  to  our  sys- 
tem. The  velocity  of  light  is,  it  will  be  remembered,  about 
300,000  kilometres  per  second,  or  such  as  to  pass  from  the 
sun  to  the  earth  in  8  minutes  18  seconds. 

The  time  required  for  light  to  reach  the  earth  from  some 
of  the  stars,  of  which  the  parallax  has  been  measured,  is  as 
follows : 


STAR. 

Years. 

STAR. 

Years. 

(x.  Ocntaui'i 

3-5 

70  Ophiuclii 

19-1 

61  Cygni 

6-7 

z   UTSCB  MQJOTIS 

24-3 

21  185  Lelande 

6-3 

Al'CtUTUS       .         ... 

25-4 

ft  Centduri  

6-9 

Y  Di'dconis  

35-1 

H  CassiopeioB  

9-4 

1830  Groombridge.  . 

35-9 

34  Groombridtve 

10-5 

Polaris      

42-4 

21  258  Lelande     

11  -9 

3077  Bradley  

46-1 

17  415  Oeltzen 

13-1 

85  Pegasi 

64-5 

Sirius            . 

16-7 

ct  AUTIOCB     

70-1 

cc  LyTffi  

17-9 

d  Dvciconis  

129-1 

CHAPTER   VI. 
CONSTRUCTION    OF    THE    HEAVENS. 

THE  visible  universe,  as  revealed  to  us  by  the  telescope,  is 
a  collection  of  many  millions  of  stars  and  of  several  thou- 
sand nebulae.  It  is  sometimes  called  the  stellar  or  sidereal 
system,  and  sometimes,  as  already  remarked,  the  stellar 
universe.  The  most  far-reaching  question  with  which 
astronomy  has  to  deal  is  that  of  the  form  and  magnitude 
of  this  system,  and  the  arrangement  of  the  stars  which 
compose  it. 

It  was  once  supposed  that  the  stars  were  arranged  on  the 
same  general  plan  as  the  bodies  of  the  solar  system,  being 
divided  up  into  great  numbers  of  groups  or  clusters,  while 
all  the  stars  of  each  group  revolved  in  regular  orbits  round 
the  centre  of  the  group.  All  the  groups  were  supposed  to 
revolve  around  some  great  common  centre,  which  was 
therefore  the  centre  of  the  visible  universe. 

But  there  is  no  proof  that  this  view  is  correct.  We  have 
already  seen  that  a  great  many  stars  are  collected  into  clus- 
ters, but  there  is  no  evidence  that  the  stars  of  these 
clusters  revolve  in  regular  orbits,  or  that  the  clusters  them- 
selves have  any  regular  motion  around  a  common  centre. 

The  first  astronomer  to  make  a  careful  study  of  the  arrangement 
of  the  stars  with  a  view  to  learn  the  structure  of  the  heavens  was  Sir 
WILLIAM  HERSCHEL. 

HERSCHEL'S  method  of  study  was  founded  on  a  mode  of  observa- 


CONSTRUCTION  OF  THE  HEAVENS. 


319 


tion  which  he  called  star-gauging.  It  consisted  in  pointing  a  power- 
ful telescope  toward  various  parts  of  the  heavens  and  ascertaining  by 
actual  count  how  thick  the  stars  were  in  each  region.  His  20-foot 
reflector  was  provided  with  such  an  eye  piece  that,  in  looking  into 
it,  he  would  see  a  portion  of  the  heavens  about  15'  in  diameter.  A 
circle  of  this  size  on  the  celestial  sphere  has  about  one  quarter  the 
apparent  surface  of  the  sun,  or  of  the  full  moon.  On  pointing  the 
telescope  in  any  direction,  a  greater  or  less  number  of  stars  were 
nearly  always  visible.  These  were  counted,  and  the  direction  in 
which  the  telescope  pointed  was  noted.  Gauges  of  this  kind  were 
made  in  all  parts  of  the  sky  at  which  he  could  point  his  instrument, 
and  the  results  were  tabulated  in  the  order  of  right  ascension. 

The  following  is  an  extract  from  the  gauges,  and  gives  the  average 
number  of  stars  in  each  tield  at  the  points  noted  in  right  ascension 
and  north-polar  distance : 


N.  P.  D. 

N.  P.  D. 

R. 

A. 

92°  to  94°. 

R.A. 

78°  to  80°. 

No.  of  Stars. 

No.  of  Stars. 

h. 

m. 

h.]          m.] 

15 

10 

9.4 

11            6 

3.1 

15 

47 

10.6 

12         44 

4.6 

16 

25 

13.6 

12         49 

3.9 

16 

37 

18.6 

14         30 

3.6 

In  this  small  table,  it  is  plain  that  a  different  law  of  clustering  or 
of  distribution  obtains  in  the  two  regions. 

The  number  of  these  stars  in  certain  portions  is  very  great.  For 
example,  in  the  Milky  Way  this  number  was  as  great  as  116, 000  stars 
in  a  quarter  of  an  hour  in  some  cases. 

HERSCHEL  supposed  at  first  that  he  completely  resolved  the  whole 
Milky  Way  into  small  stars.  This  conclusion  he  subsequently  modi- 
fied. He  says: 

"  It  is  very  probable  that  the  great  stratum  called  the  Milky  Way  is 
that  in  which  the  sun  is  placed,  though  perhaps  not  in  the  very  cen- 
tre of  its  thickness. 

"  We  gather  this  from  the  appearance  of  the  Galaxy,  which  seems 
to  encompass  the  whole  heavens,  as  it  certainly  must  do  if  the  sun  is 
within  it.  For,  suppose  a  number  of  stars  arranged  between  two 
parallel  planes,  indefinitely  extended  every  way,  but  at  a  given  con- 
siderable distance  from  each  other,  and  calling  this  a  sidereal  stratum, 
an  eye  placed  somewhere  within  it  will  see  all  the  stars  in  the  direc- 


320 


ASTRONOMY. 


lion  of  the  planes  of  the  stratum  projected  into  a  great  circle,  which 
will  appear  lucid  on  account  of  the  accumulation  of  the  stars,  while 


*                   *     ~-r"&   p  x>^                *     * 

B    s&f'  *  .   „   ^^ 

x           *           *d$f*l,      *      *   *    *  *             «^        *         * 

:-;-;::%xW  *  *'*  ;-Xv 


FIG.  93.—  HERSCHKL'S  THEORY  OF  THE  STELLAR  SYSTEM. 


the  rest  of  the  heavens,  at  the  sides,  will  only  seem  to  be  scattered 
over  with  constellations,  more  or  less  crowded,  according  to  the  dis,- 


CONSTRUCTION  OF  THE  HEAVENS.  321 

tance  of  the  planes,  or  number  of  stars  contained  in  the  thickness  or 
sides  of  the  stratum." 

Thus  in  HERSCHEL'S  figure  an  eye  at  S  within  the  stratum  a  b  will 
see  the  stars  in  the  direction  of  its  length  a  b,  or  height  c  d,  with  all 
those  in  the  intermediate  situations,  projected  into  the  lucid  circle 
A  CBD,  while  those  in  the  sides  mv,  nw,  will  be  seen  scattered  over 
the  remaining  part  of  the  heavens  MV  NW. 

"  If  the  eye  were  placed  somewhere  without  the  stratum,  at  no 
very  great  distance,  the  appearance  of  the  stars  within  it  would 
assume  the  form  of  one  of  the  smaller  circles  of  the  sphere,  which 
would  be  more  or  less  contracted  according  to  the  distance  of  the 
eye;  and  if  this  distance  were  exceedingly  increased,  the  whole 
stratum  might  at  last  be  drawn  together  into  a  lucid  spot  of  any 
shape,  according  to  the  length,  breadth,  and  height  of  the  stratum. 

"  Suppose  that  a  smaller  stratum  pq  should  branch  out  from  the 
former  in  a  certain  direction,  and  that  it  also  is  contained  between 
two  parallel  planes,  so  that  the  eye  is  contained  within  the  great 
stratum  somewhere  before  the  separation,  and  not  far  from  the  place 
where  the  strata  are  still  united.  Then  this  second  stratum  will  not 
be  projected  into  a  bright  circle  like  the  former,  but  it  will  be  seen 
as  a  lucid  branch  proceeding  from  the  first,  and  returning  into  it 
again  at  a  distance  less  than  a  semicircle. 

"  In  the  figure  the  stars  in  the  small  stratum  p  q  will  be  projected 
into  a  bright  arc  PR  It  P,  which,  after  its  separation  from  the  circle 
CBD,  unites  with  it  again  at  P. 

"If  the  bounding  surfaces  are  not  parallel  planes,  but  irregularly 
curved  surfaces,  analogous  appearances  must  result." 

The  Milky  Way,  as  we  see  it  with  the  naked  eye,  presents  the 
aspect  which  has  been  just  accounted  for.  in  its  general  appearance 
of  a  girdle  around  the  heavens  and  in  its  bifurcation  at  a  certain 
point,  and  HERSCHEL'S  explanation  of  this  appearance,  as  just  given, 
has  never  been  seriously  questioned.  One  doubtful  point  remains: 
are  the  stars  in  Fig.  93  scattered  all  through  the  space  8 — abpdl 
or  are  they  near  its  bounding  planes,  or  clustered  in  any  way  within 
this  space  so  as  to  produce  the  same  result  to  the  eye  as  if  uniformly 
distributed  ? 

HERSCHEL  assumed  that  they  were  nearly  equably  arranged  all 
through  the  space  in  question.  He  only  examined  one  other  arrange- 
ment— viz.,  that  of  a  ring  of  stars  surrounding  the  sun — and  he  pro- 
nounced against  such  an  arrangement,  for  the  reason  that  there  is 
absolutely  nothing  in  the  size  or  brilliancy  of  the  sun  to  cause  us  to 
suppose  it  to  be  the  centre  of  such  a  gigantic  system.  No  reason  ex- 
cept its  importance  to  us  personally  can  be  alleged  for  such  a  sup- 


322  ASTRONOMY. 

position.  By  the  assumptions  of  Fig.  93,  each  star  will  have  its 
own  appearance  of  a  galaxy  or  milky  way,  which  will  vary  accord- 
ing to  the  situation  of  the  star. 

Such  an  explanation  will  account  for  the  general  appearances  of 
the  Milky  Way  and  of  the  rest  of  the  sky,  supposing  the  stars  equally  or 
nearly  equally  distributed  in  space.  On  this  supposition,  the  system 
must  be  deeper  where  the  stars  appear  more  numerous. 


I 


CHAPTER  VIL 
COSMOGONY. 

A  THEORY  of  the  operations  by  which  the  universe  re- 
ceived its  present  form  and  arrangement  is  called  Cosmog- 
ony. This  subject  does  not  treat  of  the  origin  of  matter, 
but  only  of  its  transformations. 

Three  systems  of  Cosmogony  have  prevailed  among 
thinking  men  at  different  times: 

(1)  That  the  universe  had  no  origin,  but  existed  from 
eternity  in  the  form  in  which  we  now  see  it.    This  was  the 
view  of  the  ancient  philosophers. 

(2)  That  it  was  created  in  its  present  shape  in  a  mo- 
ment, out  of  nothing.     This  view  is  based  on  the  literal 
sense  of  the  words  of  the  Old  Testament. 

(3)  That  it  came  into  its  present  form  through  an  ar- 
rangement of  materials  which  were  before  "  without  form 
and  void."     This  may  be  called  the  evolution  theory.     It 
is  to  be  noticed  that  no  attempt  is  made  to  explain  the 
origin  of  the  primitive  matter. 

The  last  is  the  idea  which  has  prevailed,  and  it  receives 
many  striking  confirmations  from  the  scientific  discoveries 
of  modern  times.  The  latter  seem  to  show  beyond  all  rea- 
sonable doubt  that  the  universe  could  not  always  have 
existed  in  its  present  form  and  under  its  present  condi- 
tions ;  that  there  was  a  time  when  the  materials  composing 
it  were  masses  of  glowing  vapor,  and  that  there  will  be  a 


324  ASTRONOMY. 

time  when  the  present  state  of  things  will  cease.  The  ex- 
planation of  the  processes  through  which  this  occurs  is 
sometimes  called  the  nebular  hypothesis.  It  was  first  pro- 
pounded by  the  philosophers  SWEDEXBORG,  KAXT,  and 
LAPLACE,  and,  although  since  greatly  modified  in  detail, 
their  views  have  in  the  main  been  retained  until  the 
present  time. 

We  shall  begin  its  consideration  by  a  statement  of  the 
various  facts  which  appear  to  show  that  the  earth  and 
planets,  as  well  as  the  sun,  were  once  a  fiery  mass. 

The  first  of  these  facts  is  the  gradual  but  uniform  in- 
crease of  temperature  as  we  descend  into  the  interior  of 
the  earth.  Wherever  mines  have  been  dug  or  wells  sunk 
to  a  great  depth,  the  temperature  increases  as  we  go  down- 
ward at  the  rate  of  about  one  degree  centigrade  to  every  30 
metres,  or  one  degree  Fahrenheit  to  every  50  feet.  The 
rate  differs  in  different  places,  but  the  general  average  ie 
near  this.  The  conclusion  which  we  draw  from  this  may 
not  at  first  sight  be  obvious,  because  it  may  seem  that  the 
earth  might  always  have  shown  this  same  increase  of  tem- 
perature. But  there  are  several  results  which  a  little 
thought  will  make  clear,  although  their  complete  establish- 
ment requires  the  use  of  the  higher  mathematics. 

The  first  result  is  that  the  increase  of  temperature  can- 
not be  merely  superficial,  but  must  extend  to  a  great 
depth,  probably  even  to  the  centre  of  the  earth.  If  it  did 
not  so  extend,  the  heat  would  have  all  been  lost  long  ages 
ago  by  conduction  to  the  interior  and  by  radiation  from 
the  surface.  It  is  certain  that  the  earth  has  not  received 
any  great  supply  of  heat  from  outside  since  the  earliest 
geological  ages,  because  such  an  accession  of  heat  at  the 
earth's  surface  would  have  destroyed  all  life,  and  even 


COSMOGONY.  325 

melted  all  the  rocks.  Therefore,  whatever  heat  there  is 
in  the  interior  of  the  earth  must  have  been  there  from  be- 
fore the  commencement  of  life  on  the  globe,  and  remained 
through  all  geological  ages. 

The  interior  of  the  earth  being  hotter  than  its  surface, 
and  hotter  than  the  space  around  it,  must  be  losing  heat, 
We  know  by  the  most  familiar  observation  that  if  any  ob- 
ject is  hot  inside,  the  heat  will  work  its  way  through  to  the 
surface  by  the  process  of  conduction.  Therefore,  since  the 
earth  is  a  great  deal  hotter  at  the  depth  of  30  metres  than 
it  is  at  the  surface,  heat  must  be  continually  coming  to  the 
surface.  On  reaching  the  surface,  it  must  be  radiated  off 
into  space,  else  the  surface  would  have  long  ago  become 
as  hot  as  the  interior.  Moreover,  this  loss  of  heat  must 
have  been  going  on  since  the  beginning,  or  at  least  since 
a  time  when  the  surface  was  as  hot  as  the  interior.  Thus,  if 
we  reckon  backward  in  time,  we  find  that  there  must  have 
been  more  and  more  heat  in  the  earth  the  further  back 
we  go,  so  that  we  must  finally  reach  back  to  a  time  when 
it  was  so  hot  as  to  be  molten,  and  then  again  to  a  time 
when  it  was  so  hot  as  to  be  a  mass  of  fiery  vapor. 

The  second  fact  is  that  we  find  the  sun  to  be  cooling  off 
like  the  earth,  only  at  an  incomparably  more  rapid  rate. 
The  sun  is  constantly  radiating  heat  into  space,  and,  so  far 
as  we  can  ascertain,  receiving  none  back  again.  A  small 
portion  of  this  heat  reaches  the  earth,  and  on  this  portion 
depends  the  existence  of  life  and  motion  on  the  earth's  sur- 
face. The  quantity  of  heat  which  strikes  the  earth  is  only 
about  OTFinsWiroT  of  that  which  the  sun  radiates.  This 
fraction  expresses  the  ratio  of  the  apparent  surface  of  the 
earth,  as  seen  from  the  sun,  to  that  of  the  whole  celestial 
sphere. 


326  ASTRONOMY. 

Since  the  sun  is  losing  heat  at  this  rate,  it  must  have  had 
more  heat  yesterday  than  it  has  to-day  ;  more  two  days  ago 
than  it  had  yesterday,  and  so  on.  Thus  calculating  back- 
ward, we  find  that  the  further  we  go  back  into  time  the 
hotter  the  sun  must  have  been.  Since  we  know  that  heat 
expands  all  bodies,  it  follows  that  the  sun  must  have  been 
larger  in  past  ages  than  it  is  now,  and  we  can  trace  back 
this  increase  in  size  without  limit.  Thus  we  are  led  to  the 
conclusion  that  there  must  have  been  a  time  when  the  sun 
filled  up  the  space  now  occupied  by  the  planets,  and  must 
have  been  a  very  rare  mass  of  glowing  vapor.  The  plan- 
ets could  not  then  have  existed  separately,  but  must  have 
formed  a  part  of  this  mass  of  vapor.  The  latter  was  there- 
fore the  material  out  of  Avhich  the  solar  system  was 
formed. 

The  same  process  may  be  continued  into  the  future. 
Since  the  sun  by  its  radiation  is  constantly  losing  heat,  it 
must  grow  cooler  and  cooler  as  ages  advance,  and  must 
finally  radiate  so  little  heat  that  life  and  motion  can  no 
longer  exist  on  our  globe. 

The  third  fact  is  that  the  revolutions  of  all  the  planets 
around  the  sun  take  place  in  the  same  direction  and  in 
nearly  the  same  plane.  We  have  here  a  similarity  amongst 
the  different  bodies  of  the  solar  system,  which  must  have 
had  an  adequate  cause,  and  the  only  cause  which  lias  ever 
been  assigned  is  found  in  the  nebular  hypothesis.  This 
hypothesis  supposes  that  the  sun  and  planets  were  once 
a  great  mass  of  vapor,  as  large  as  or  larger  than  the  present 
solar  system,  revolving  on  its  axis  in  the  same  plane  in 
which  the  planets  now  revolve. 

The  fourth  fact  is  seen  in  the  existence  of  nebulae.  The 
spectroscope  shows  these  bodies  to  be  masses  of  glowing 


COSMOGONY. 


vapor.  We  thus  actually  see  matter  in  the  celestial  spaces 
under  the  very  form  in  which  the  nebular  hypothesis  sup- 
poses the  matter  of  our  solar  system  to  have  once  existed. 
Since  these  masses  of  vapor  are  so  hot  as  to  radiate  light 
and  heat  through  the  immense  distance  which  separates  us 
from  them,  they  must  be  gradually  cooling  off.  This  cool- 
ing must  at  length  reach  a  point  when  they  will  cease  to 
be  vaporous  and  condense  into  objects  like  stars  and 
planets.  We  know  that  every  star  in  the  heavens  radiates 
heat  as  our  sun  does.  In  the  case  of  the  brighter  stars  the 
heat  radiated  has  been  made  sensible  in  the  foci  of  our 
telescopes  by  means  of  the  thermo-multiplier.  All  the 
stars  must,  like  the  sun,  be  radiating  heat  into  space. 

A  fifth  fact  is  afforded  by  the  physical  constitution  of 
the  planets  Jupiter  and  Saturn.  The  telescopic  examina- 
tion of  these  planets  shows  that  changes  on  their  surfaces 
are  constantly  going  on  with  a  rapidity  and  violence  to 
which  nothing  on  the  surface  of  our  earth  can  compare. 
Such  operations  can  be  kept  up  only  through  the  agency  of 
heat  or  some  equivalent  form  of  energy.  But  at  the  dis- 
tance of  Jupiter  and  Saturn  the  rays  of  the  sun  are  entirely 
insufficient  to  produce  changes  so  violent.  We  are  there- 
fore led  to  infer  that  Jupiter  and  Saturn  must  be  hot 
bodies,  and  must  therefore  be  cooling  off  like  the  sun, 
stars,  and  earth. 

We  are  thus  led  to  the  general  conclusion  that,  so  far 
as  our  knowledge  extends,  nearly  all  the  bodies  of  the 
universe  are  hot,  and  are  cooling  off  by  radiating  their 
heat  into  space. 

The  idea  that  the  heat  radiated  by  the  sun  and  stars  may 
in  some  way  be  collected  and  returned  to  them  by  the 
operation  of  known  natural  laws  is  equally  untenable.  It 


328  ASTRONOMY. 

is  a  fundamental  principle  of  the  laws  of  heat  that  "  the 
latter  can  never  pass  from  a  cooler  to  a  warmer  body/'  and 
that  a  body  can  never  grow  warm  or  acquire  heat  in  a  space 
that  is  cooler  than  the  body  is  itself.  All  differences  of 
temperature  tend  to  equalize  themselves,  and  the  only 
state  of  things  to  which  the  universe  can  tend,  under  its 
present  laws,  is  one  in  which  all  space  and  all  the  bodies  con- 
tained in  space  are  at  a  uniform  temperature,  and  then  all 
motion  and  change  of  temperature,  and  hence  the  condi- 
tions of  vitality,  must  cease.  And  then  all  such  life  as  ours 
must  cease  also  unless  sustained  by  entirely  new  methods. 

The  general  result  drawn  from  all  these  laws  and  facts 
is,  that  there  was  once  a  time  when  all  the  bodies  of  the 
universe  formed  either  a  single  mass  or  a  number  of  masses 
of  fiery  vapor,  having  slight  motions  in  various  parts,  and 
different  degrees  of  density  in  different  regions.  A  grad- 
ual condensation  around  the  centres  of  greatest  density  then 
went  on  in  consequence  of  the  cooling  and  the  mutual  at- 
traction of  the  parts,  and  thus  arose  a  great  number  of 
nebulous  masses.  One  of  these  masses  formed  the  ma- 
terial out  of  which  the  sun  and  planets  are  supposed  to 
have  been  formed.  It  was  probably  at  first  nearly  glob- 
ular, of  nearly  equal  density  throughout,  and  endowed 
with  a  very  slow  rotation  in  the  direction  in  which  the 
planets  now  move.  As  it  cooled  oC,  it  grew  smaller  and 
smaller,  and  its  velocity  of  rotation  increased  in  rapidity. 

The  rotating  mass  we  have  described  must  have  had  an  axis 
around  which  it  rotated,  and  therefore  an  equator  defined 
as  being  everywhere  90°  from  this  axis.  In  consequence 
of  the  increase  in  the  velocity  of  rotation,  the  centrifugal 
force  would  also  be  increased  as  the  mass  grew  smaller. 
This  force  varies  as  the  radius  of  the  circle  described  by 


COSMOGONY.  329 

any  particle  multiplied  by  the  square  of  its  angular  velocity. 
Hence  when  the  masses,  being  reduced  to  half  the  radius, 
rotated  four  times  as  fast,  the  centrifugal  force  at  the  equa- 
tor would  be  increased  -Jx4a,  or  eight  times.  The  gravi- 
tation of  the  mass  at  the  surface,  being  inversely  as  the 
square  of  the  distance  from  the  centre,  or  of  the  radius, 
would  be  increased  four  times.  Therefore  as  the  masses 
continue  to  contract,  the  centrifugal  force  increases  at  a 
more  rapid  rate  than  the  central  attraction.  A  time  would 
therefore  come  when  they  would  balance  each  other  at  the 
equator  of  the  mass.  The  mass  would  then  cease  to  con- 
tract at  the  equator,  but  at  the  poles  there  would  be  no 
centrifugal  force,  and  the  gravitation  of  the  mass  would 
grower  stronger  and  stronger.  In  consequence  the  mass 
would  at  length  assume  the  form  of  a  lens  or  disk  very  thin 
in  proportion  to  its  extent.  The  denser  portions  of  this 
lens  would  gradually  be  drawn  toward  the  centre,  and  there 
more  or  less  solidified  by  the  process  of  cooling.  A  point 
would  at  length  be  reached,  when  solid  particles  would  begin 
to  be  formed  throughout  the  whole  disk.  These  would  grad- 
ually condense  around  each  other  and  form  a  single  planet,  or 
they  might  break  up  into  small  masses  and  form  a  group  of 
planets.  As  the  motion  of  rotation  would  not  be  altered 
by  these  processes  of  condensation,  these  planets  would  all 
be  rotating  around  the  central  part  of  the  mass,  which  is 
supposed  to  have  condensed  into  the  sun. 

It  is  supposed  that  at  first  these  planetary  masses,  being 
very  hot,  were  composed  of  a  central  mass  of  those  sub- 
stances which  condensed  at  a  very  high  temperature,  sur- 
rounded by  the  vapors  of  those  substances  which  were 
more  volatile.  We  know,  for  instance,  that  it  takes  a  much 
higher  temperature  to  reduce  lime  and  platinum  to  vapor 


330  ASTRONOMY. 

than  it  does  to  reduce  iron,  zinc,  or  magnesium.  There- 
fore, in  the  original  planets,  the  limes  and  earths  would 
condense  first,  while  many  other  metals  would  still  be  in 
a  state  of  vapor.  The  planetary  masses  would  each  be 
affected  by  a  rotation  increasing  in  rapidity  as  they  grew 
smaller,  and  would  at  length  form  masses  of  melted  metals 
and  vapors  in  the  same  way  as  the  larger  mass  out  of  which 
the  sun  and  planets  were  formed.  These  masses  would 
then  condense  into  a  planet,  with  satellites  revolving 
around  it,  just  as  the  original  mass  condensed  into  sun  and 
planets. 

At  first  the  planets  would  be  so  hot  as  to  be  in  a  molten 
condition,  each  of  them  probably  shining  like  the  sun. 
They  would,  however,  slowly  cool  off  by  the  radiation  of 
heat  from  their  surfaces.  So  long  as  they  remained  liquid, 
the  surface,  as  fast  as  it  grew  cool,  would  sink  into  the  in- 
terior on  account  of  its  greater  specific  gravity,  and  its 
place  would  be  taken  by  hotter  material  rising  from  the 
interior  to  the  surface,  there  to  cool  off  in  its  turn.  There 
would,  in  fact,  be  a  motion  something  like  that  which 
occurs  when  a  pot  of  cold  water  is  set  upon  the  fire  to  boil. 
Whenever  a  mass  of  wator  at  the  bottom  of  the  pot  is 
heated,  it  rises  to  the  surface,  and  the  cool  water  moves 
down  to  take  its  place.  Thus,  on  the  whole,  so  long  as 
the  planet  remained  liquid,  it  would  cool  off  equally 
throughout  its  whole  mass,  owing  to  the  constant  motion 
from  the  centre  to  the  circumference  and  back  again.  A 
time  would  at  length  arrive  when  many  of  the  earths  and 
metals  would  begin  to  solidify.  At  first  the  solid  particles 
would  be  carried  up  and  down  with  the  liquid.  A  time 
would  finally  arrive  when  they  would  become  so  large 
and  numerous,  and  the  liquid  part  of  the  general  mass 


COSMOGONY.  331 

become  so  viscid,  that  the  motion  would  be  obstructed. 
The  planet  would  then  begin  to  solidify.  Two  views 
have  been  entertained  respecting  the  process  of  solidifica- 
tion. 

According  to  one  view,  the  whole  surface  of  the  planet 
would  solidify  into  a  continuous  crust,  as  ice  forms  over  a 
pond  in  cold  weather,  while  the  interior  was  still  in  a 
molten  state.  The  interior  liquid  could  then  no  longer 
come  to  the  surface  to  cool  off,  and  could  lose  no  heat 
except  what  was  conducted  through  this  crust.  Hence 
the  subsequent  cooling  would  be  much  slower,  and  the 
globe  would  long  remain  a  mass  of  lava,  covered  over  by 
a  comparatively  thin  solid  crust  like  that  on  which  we 
live. 

The  other  view  is  that,  when  the  cooling  attained  a  cer- 
tain stage,  the  central  portion  of  the  globe  would  be 
solidified  by  the  enormous  pressure  of  the  superincumbent 
portions,  while  the  exterior  was  still  fluid,  and  that  thus 
the  solidification  would  take  place  from  the  centre  out- 
ward. 

It  is  still  an  unsettled  question  whether  the  earth  is  now 
solid  to  its  centre,  or  whether  it  is  a  great  globe  of  molten 
matter  with  a  comparatively  thin  crust.  Astronomers  and 
physicists  incline  to  the  former  view  ;  geologists  to  the  lat- 
ter one.  Whichever  view  may  be  correct,  it  appears  cer- 
tain that  there  are  great  lakes  of  lava  in  the  interior  from 
which  volcanoes  are  fed. 

It  must  be  understood  that  the  nebular  hypothesis,  as  we 
have  explained  it,  is  not  a  perfectly  established  scientific 
theory,  but  only  a  philosophical  conclusion  founded  on  the 
widest  study  of  nature,  and  pointed  to  by  many  otherwise 
disconnected  facts.  The  widest  generalization  associated 


332  ASTRONOMY. 

with  it  is  that,  so  far  as  we  can  see,  the  universe  is  not  self- 
sustaining,  but  is  a  kind  of  organism  which,  like  all  other 
organisms  we  know  of,  must  come  to  an  end  in  consequence 
of  those  very  laws  of  action  which  keep  it  going.  It  must 
have  had  a  beginning  within  a  certain  number  of  years 
which  we  cannot  yet  calculate  with  certainty,  but  which 
cannot  much  exceed  20,000,000,  and  it  must  end  in  a  chaos 
of  cold,  dead  globes  at  a  calculable  time  in  the  future, 
when  the  sun  and  stars  shall  have  radiated  away  all  their 
heat,  unless  it  is  re-created  by  the  action  of  forces  of  which 
we  at  present  know  nothing. 


APPENDIX. 


SPECTRUM  ANALYSIS. 

ALTHOUGH  the  subject  of  Spectrum  Analysis  belongs 
properly  to  physics,  a  brief  account  of  its  relations  to  astron- 
omy may  be  useful  here, 

To  understand  the  instruments  and  methods  of  Spectrum 
Analysis  it  will  be  necessary  to  recall  the  optical  properties 
of  a  prism,  which  are  demonstrated  in  all  treatises  on  phy- 
sics. 

The  Prism. — When  parallel  rays  of  homogeneous  light, 


FIG.  94. 

red  for  example,  fall  on  a  face  of  a  prism  they  are  bent  out 
of  their  course,  and  when  they  emerge  from  the  prism  they 


334  APPENDIX. 

are  again  bent,  but  they  still  remain  parallel;  thus  the  rays 
r  r,  r"r" ,  are  bent  into  the  final  direction  r  V.  This  is  true 
for  parallel  rays  of  every  color.  They  remain  parallel  after 
deviation  by  the  prism.  This  can  be  shown  by  experiment. 
If  the  incident  rays  r  r,  in  Fig.  94,  are  red,  they  will  come 
to  the  screen  at  r'r'.  If  they  are  violet  rays,  they  will 
come  to  v'v'  on  the  screen,  after  having  been  bent  more 
from  their  original  course  than  the  red  rays.  The  violet 
rays,  with  the  shortest  wave-length,  are  the  most  refrangi- 
ble. The  red,  with  the  longest  wave-length,  are  the  least 
refrangible. 

The  experiments  of  Sir  ISAAC  NEWTON  (1704)  proved 
that  white  light  (as  sunlight,  moonlight,  starlight)  was 
not  simple  but  compound.  That  is,  white  light  is  made  up 
of  light  of  different  wave-lengths.  Difference  of  wave-length 
shows  itself  to  the  eye  as  difference  of  color.  Seven  colors  were 
distinguished  by  NEWTON;  viz.,  violet,  indigo,  blue,  green, 
yellow,  orange,  red.  (Memorize  these  in  order.  It  is  the 
order  of  the  colors  in  the  rainbow.)  If  parallel  rays  of 
white  light,  as  sunlight,  r  r,  fall  on  a  prism,  the  red  rays  of 
this  beam  will  still  fall  at  r'r',  and  the  violet  rays  will  fall 
at  v'v'.  Between  v'  and  r'  the  other  rays  will  fall,  in  the 
order  just  given;  that  is,  in  the  order  of  their  refrangibility. 
The  rainbow-colored  streak  on  the  screen  is  called  the 
spectrum;  it  is  a  solar,  a  lunar,  or  a  stellar  spectrum  ac- 
cording as  the  source  of  the  rays  is  the  sun,  moon,  or  a  star. 
The  solar  spectrum  is  very  bright;  the  lunar  spectrum  is 
much  fainter;  and  the  spectrum  of  a  star  is  far  fainter  than 
either. 

If  we  let  parallel  rays,  rr,  of  red  light  come  through  a 
circular  hole  at  Q,  they  will  form  a  circular  image  of  the 
hole  at  r'r'.  If  the  hole  is  square  or  triangular,  a  square  or 


APPENDIX.  335 

a  triangular  image  will  be  formed.  If  it  is  a  narrow  slit,  a 
narrow  streak  of  red  light  will  be  projected  at  r'r'. 

When  white  light  is  passed  through  a  circular  hole  at  Q, 
circular  images  of  the  hole  are  formed  all  along  the  line 
r V  to  ?;V:  the  red  images  at  r'r',  the  orange,  yellow, 
green,  blue  images  in  succession,  and  the  violet  image  at 
v'v'.  If  the  hole  is  of  any  size  these  imnges  will  overlap, 
so  that  the  colors  are  not  pure.  If  white  light  falls  through 
a  narrow  slit  at  Q,  placed  parallel  to  the  edge  A  of  the 
prism,  the  purest  spectrum  is  obtained.  The  different 
spectra  do  not  overlap. 

FRAUNHOFER  tried  this  experiment  in  1804,  and  he 
found  that  the  spectrum  of  the  sun  was  interrupted  by  certain 
dark  lines,  fixed  in  relative  position.  These  are  the  Fraun- 
hofer  lines,  so  called.  He  made  a  map  of  the  solar  spec- 
trum, and  on  the  map  he  placed  the  various  lines  in  their 
proper  places,  These  lines  appear  in  the  same  relative 
position  no  matter  whether  a  slit  or  a  very  small  circular 
hole  is  used,  and  they  belong  to  the  incident  light  and  are 
not  produced  by  the  apparatus.  This  simply  renders  them 
visible.  They  are  not  seen  when  the  light  comes  through 
wide  apertures,  on  account  of  the  overlapping  of  the  vari- 
ous images. 

The  Spectroscope. — A  spectroscope  consists  essentially  of 
one  or  more  prisms  (or  any  other  device,  as  a  diffraction 
grating)  by  means  of  which  a  spectrum  is  produced;  of 
a  means  to  make  the  spectrum  pure  (a  slit  and  collimator), 
and  of  a  means  to  see  it  well  (a  small  telescope). 

Fig.  95  shows  the  arrangement  of  a  one-prism  spectro- 
scope. The  light  enters  the  slit  S,  which  is  exactly  in 
the  focus  of  the  objective  A  of  the  collimator.  The  rays 
therefore  emerge  from  A  in  parallel  lines.  They  are  de- 


336 


APPENDIX, 


viated  by  the  prism  P,  and  enter  the  objective  B,  forming 
an  image  of  the  spectrum  at  0,  which  is  viewed  by  the  eye 


Fro.  95. 


The  Solar  Spectrum. — Part  of  this  image  (of  the  solar 
spectrum)  is  shown  in  Fig.  96,  except  as  to  color.     The 


A    a    B     C 


E   b 


FIG.  96. 


various  colors  extend  in  succession  from  end  to  end  of  the 
spectrum.  In  each  color  are  certain  dark  lines  which  have 
a  definite  position.  The  most  conspicuous  of  these  lines 
are  called  the  Fraunhofer  lines,  and  a^e  lettered  A,  B,  C, 
D,  J2,  F,  G,  H.  A  is  below  the  easily  visible  red,  B  is  at 
its  lower  edge,  G  is  near  the  middle  of  the  red,  D  is  a  double 


APPEKD1X  337 

line  in  the  orange,  Eis  in  the  green,  F is  in  the  blue,  G  in  the 
indigo,  and  Hm  the  violet.  There  are  at  least  500  lines 
besides  which  can  be  seen  with  spectroscopes  of  moderate 
power.  Each  and  every  one  of  these  has  a  definite  position. 

When  the  instrument  drawn  in  Fig.  95  is  pointed  toward 
the  sun  (so  that  the  sun's  rafs  fall  on  S),  the  spectrum 
seen  is  that  of  the  whole  sun.  If  we  wish  to  examine  the 
spectrum  of  &  part  of  the  sun,  as  of  a  spot  for  example,  we 
must  attach  the  whole  instrument  (Fig.  95)  to  a  telescope, 
so  that  S  is  in  the  principal  focal  plane  of  the  telescope- 
objective  (page  62).  An  image  of  the  sun  will  then  be 
formed  by  the  telescope-objective  on  the  slit  plate  8,  and 
the  light  from  any  part  of  that  image  can  be  examined  at 
will.  The  spectroscope  is  used  in  the  same  way  to  examine 
faint  stars.  We  employ  a  telescope  in  this  case  so  that  its 
objective  may  collect  more  light  and  present  it  at  the  slit 
of  the  spectroscope. 

Spectra  of  Solids  and  Gases.— A  solid  body,  heated  so 
intensely  as  to  give  off  light,  has  a  continuous  spectrum. 
That  is,  there  are  no  Fraunhofer  lines  in  it,  but  prismatic 
colors  only.  A  gaseous  body,  heated  so  intensely  as  to  give 
off  light,  has  a  discontinuous  spectrum.*  That  is,  the  colors 
red  to  violet  are  no  longer  seen,  but  on  a  dark  background 
the  spectrum  shows  one  or  more  bright  lines. 

These  lines  have  a  definite  relative  position  and  are 
characteristic  of  the  particular  gas.  The  vapor  of  sodium, 
for  example,  gives  two  bright  lines,  whose  relative  position 
is  fixed.  These  facts  can  be  shown  by  laboratory  experi- 
ments. Another  experiment  must  be  cited.  If  the  source 
of  light  is  a  solid  body,  intensely  heated,  the  spectroscope 
will  show  a  continuous  spectrum,  without  lines,  as  has  been 

*  Unless  under  great  pressure,  when  the  spectrum  is  continuous  as  in  the  case 
of  our  sun,  and  of  stars  of  similar  constitution, 


338  APPENDIX. 

said.  If  between  the  solid  body  and  the  slit  of  the  spec- 
troscope we  place  a  glass  vessel  containing  the  vapor  of 
sodium,  the  spectrum  will  no  longer  be  without  lines.  Two 
dark  lines  will  appear  in  the  orange.  If  we  remove  the 
vapor  of  sodium,  the  lines  will  go  also.  They  are  produced 
by  the  absorptive  action  of  this  vapor  on  the  incident  light. 

If  we  register  exactly  the  spot  in  the  field  of  view  of  the 
spectroscope  where  each  of  these  dark  lines  appears,  and  if 
we  then  remove  the  sodium  vapor  and  replace  the  solid 
body  (the  source  of  light)  by  intensely  heated  sodium 
vapor,  we  shall  find  the  new  spectrum  to  be  composed  of 
two  bright  lines,  as  has  been  said;  but  these  two  bright 
lines  will  occupy  exactly  the  same  places  in  the  field  of  view 
that  the  two  dark  lines  formerly  occupied. 

The  two  dark  lines  are  a  sign  of  the  kind  of  light  that  is 
absorbed  by  sodium  vapor;  the  two  bright  lines  are  a  sign 
of  the  kind  of  light  that  is  emitted^  sodium  vapor.  These 
two  kinds  are  the  snme.  What  is  true  of  sodium  vapor  is 
true  of  every  gas.  It  absorbs  light  of  the  same  kind  (wave- 
length) as  that  which  it  emits. 

If  a  spectroscopist  had  to  determine  what  kind  of  gas 
was  in  a  certain  jar,  he  might  do  it  in  two  ways.  He  might 
heat  it  intensely,  and  measure  the  positions  of  the  bright 
lines  of  its  spectrum;  or  he  might  place  the  gas  between  the 
slit  of  his  spectroscope  and  a  highly  heated  solid  body,  and 
agjiin  measure  the  positions  of  the  dark  lines  of  its 
absorption-spectrum.  The  measures  and  thus  the  positions 
of  the  lines  will  be  the  same  in  both  cases.  By  comparing 
the  measures  with  previous  measures  for  known  gases,  the 
name  of  the  particular  gas  in  question  would  become  known 
to  him.  New  chemical  elements  have  been  discovered  in 
this  way. 


A  PPENDIX.  339 

Comparison  of  the  Spectra  of  Incandescent  Gases  with 
the  Solar  Spectrum. — Laboratory  experiments  show  the  posi- 
tions of  the  spectral  lines  characteristic  of  each  gas  or  vapor. 
The  positions  of  the  dark  lines  in  the  solar  spectrum  are 
also  known  with  accuracy.  It  is  found  that  nearly  every 
one  of  the  thousands  of  dark  lines  of  the  solar  spectrum 
has  a  position  corresponding  exactly  to  that  of  some  one 
of  the  lines  of  some  gas  or  of  the  vapor  of  some  metal.  For 
example,  the  vapor  of  iron  has  over  400  lines,  whose  posi- 
tions are  accurately  known.  In  the  solar  spectrum  there 
are  400  lines  whose  positions  precisely  correspond  to  the 
lines  of  iron  vapor.  The  same  is  true  of  many  other 
substances,  hydrogen,  sodium,  potassium,  magnesium, 
nickel,  copper,  etc.  etc. 

From  this  it  is  inferred  that  the  sun's  atmosphere  con- 
tains the  metal  iron  in  an  incandescent  state,  as  well  as  the 
vapors  of  the  other  substances  named. 

Let  us  see  the  process  of  reasoning  which  led  KIRCHHOFF 
and  BTOSEN  (1859)  to  this  interpretation  of  the  observation. 

We  have  seen  (Part  II.,  Chap.  II.)  that  the  sun  is  com- 
posed of  a  luminous  surface,  the  photosphere,  surrounded 
by  a  gaseous  envelope.  The  photosphere  alone  would  give  a 
continuous  spectrum  (with  no  dark  lines).  The  gaseous 
envelope  will  absorb  the  kind  of  light  that  it  would  itself 
emit.  The  absorption  is  only  selective,  and  it  is  character- 
istic. If  a  solid  incandescent  body  were  placed  in  a  labo- 
ratory and  surrounded  by  the  vapors  of  iron,  hydrogen, 
sodium,  etc.,  we  should  see  the  same  spectrum  that  we 
do  see  when  we  examine  the  sun. 

The  kind  of  evidence  is  easily  understood  from  the  fore- 
going. Only  the  spectroscopist  can  fully  appreciate  the 
amount  of  it.  The  resulting  inference  that  the  sun's 


340  APPENDIX. 

atmosphere  contains  the  vapors  of  the  metals  named  is 
certain.  These  vapors  exist  uncombined  in  the  sun's  at- 
mosphere. The  temperature  is  too  high  to  allow  their 
chemical  combination. 

RESULTS  OF  SPECTROSCOPIC  OBSERVATIONS. 

The  Sun.— The  rays  which  come  from  the  edges  of  the 
sun  give  lines  more  marked  and  definite  than  those  from 
the  centre. 

This  shows  that  rays  from  the  limb  traverse  a  greater 
thickness  of  the  absorbing  layer.  In  Fig.  36,  suppose  SE 
to  be  the  sun's  radius,  and  SMto  be  the  radius  of  his  at- 
mosphere. A  person  stationed  at  E'  and  looking  at  the 
sun  along  the  lines  E'S  and  E'E  would  see  the  centre  of 
the  sun's  disk  by  means  of  a  ray  which  had  traversed  the 
distance  S M  —  SE  only;  while  the  ray  from  the  edge 
E  would  have  traversed  a  greater  distance  and  would  have 
suffered  a  greater  absorption.  The  sun's  absorbing  atmos- 
phere ("reversing  layer")  is  very  thin,  about  2000  kilometres 
only.  This  layer  is  seen  for  an  instant  only,  at  the  begin- 
ning and  end  of  a  solar  eclipse.  The  spectroscopic  ex- 
amination of  sun-spots  confirms  what  has  already  been  said 
of  them.  (Part  II.,  Chapter  II.) 

The  solar  protuberances  are  now  daily  studied  by  the 
spectroscope  at  various  observatories.  An  explanation  of 
the  method  of  viewing  them,  etc.,  is  given  on  pp.  215,  216. 

The  Stars. — The  spectroscopic  examination  of  stars  (ana 
star  clusters)  shows  the  fixed  stars  to  be  bodies  of  the  same 
general  nature  as  our  sun  (see  pp.  309,  310).  Not  only 
have  the  elements  composing  many  of  the  fixed  stars  been 
determined  by  the  spectroscope,  but  the  velocity  of  the 
motion  of  stars  towards  or  from  the  earth  has  been  fixed. 
(See  pp.  310,  31U 


APPENDIX.  341 

Comets  and  Nebulae. — The  spectra  of  comets  and  nebulae 
are  also  studied,  and  the  principal  results  of  observation 
are  given  on  pp.  276,  277,  and  309. 

The  Planets. — The  physical  constitution  of  the  planets  as 
revealed  by  the  spectroscope  is  treated  in  Part  II.,  Chapter 
XL,  pp.  261  to  264. 

The  Moon. — The  spectrum  of  the  moon  is  simply  an  en- 
feebled solar  spectrum  without  any  lines  of  selective  ab- 
sorption, which  is  one  proof  that  the  moon  has  no  atmos- 
phere. 

Meteors. — The  gases  shut  up  in  the  cavities  of  meteoric 
stones  have  been  spectroscopically  examined,  and  they  show 
the  characteristic  comet  spectrum.  This  gives  a  new  proof 
of  the  connection  between  comets  and  meteors. 


DESCRIPTION  AND  MAPS  OF  THE  CONSTELLA- 
TIONS. 

Every  intelligent  person  desires  to  possess  some  know- 
ledge of  the  names  and  forms  of  the  principal  constella- 
tions. We  therefore  present  a  brief  description  of  the 
more  striking  ones,  illustrated  by  figures,  so  that  the 
reader  may  be  able  to  recognize  them  when  he  sees  them. 

We  begin  with  the  constellations  near  the  pole,  because 
they  can  be  seen  on  any  clear  night,  while  the  southern 
ones  can,  for  the  most  part,  only  be  seen  during  certain 
seasons,  or  at  certain  hours  of  the  night.  Figure  97  shows 
all  the  stars  within  50°  of  the  pole  down  to  the  fourth 
magnitude  inclusive.  The  Roman  numerals  around  the 
margin  show  the  meridians  of  right  ascension,  one  for 
every  hour.  In  order  to  have  the  map  represent  the 
northern  constellations  exactly  as  they  are,  it  must  be 
held  so  that  the  hour  of  sidereal  time  at  which  the  observer 
is  looking  at  the  heavens  shall  be  at  the  top  of  the  map. 
Supposing  the  observer  to  look  at  nine  o'clock  (mean  solar 
time)  in  the  evening,  the  months  around  the  margin  of 
the  map  show  the  regions  near  the  zenith.  He  has  there- 
fore only  to  hold  the  map  with  the  month  upward  and  face 
the  north,  when  he  will  have  the  northern  heavens  as  they 
appear,  except  that  the  stars  near  the  bottom  of  the  map 
will  be  cut  off  by  the  horizon. 

The  first  constellation  to  be  looked  for  is  Ursa  Major, 


APPENDIX. 


343 


Fio.  97. — MAP  OF  THE  NORTHERN  CONSTELLATIONS. 


344  APPENDIX. 

the  Great  Bear,  familiarly  known  as  "the  Dipper."  The 
two  extreme  stars  in  this  constellation  point  toward  the 
pole-star,  as  already  explained  in  the  opening  chapter. 

Ursa  Minor,  sometimes  called  "  the  Little  Dipper/'  is 
the  constellation  to  which  the  pole-star  belongs.  About 
15°  from  the  pole,  in  right  ascension  XV  hours,  is  a  star 
of  the  second  magnitude,  ft  Ursce  Minoris,  about  as  bright 
as  the  pole-star.  A  curved  row  of  three  small  stars  lies 
between  these  two  bright  ones,  and  forms  the  handle  of 
the  supposed  dipper. 

Cassiopeia,  or  "  the  Lady  in  the  Chair,"  is  near  hour  I 
of  right  ascension,  on  the  opposite  side  of  the  pole-star 
from  Ursa  Major,  and  at  nearly  the  same  distance.  The 
six  brighter  stars  are  supposed  to  bear  a  rude  resemblance 
to  a  chair. 

Jn  hour  III  of  right  ascension  is  situated  the  constella- 
tion Perseus,  about  10°  further  from  the  pole  than  Cas- 
siopeia. The  Milky  Way  passes  through  these  two  con- 
stellations. 

Draco,  the  Dragon,  is  formed  principally  of  a  long  row 
of  stars  lying  between  Ursa  Major  and  Ursa  Minor.  The 
hcud  of  the  monster  is  formed  of  the  northernmost  three 
of  four  bright  stars  arranged  at  the  corners  of  a  lozenge 
between  XVII  and  XVIII  hours  of  right  ascension. 

Cepheus  is  on  the  opposite  side  of  Cassiopeia  from  Per- 
seus, lying  in  the  Milky  Way,  about  XXII  hours  of  right 
ascension.  It  is  not  a  brilliant  constellation. 

Other  constellations  near  the  pole  are  Camelopardalis, 
Lynx,  and  Lacerta  (the  Lizard),  but  they  contain  only 
small  stars. 

Figure  98  shows  the  equatorial  stars  situated  between  30° 
north  and  30°  south  declination.  The  forms  of  the  con- 


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APPENDIX. 

stellations  are  indicated  by  dotted  lines, 
men  and  animals  with  which  the  ancients  covered  the  sky 
are  omitted.  The  Latin  name  within  each  boundary  is  the 
name  of  the  constellation.  The  Greek  letters  serve  to 
name  the  brightest  stars  (p.  292).  The  parallels  of  decli- 
nation (for  every  15°)  and  the  hour-circles  (every  hour)  are 
laid  down. 

The  magnitudes  of  the  stars  are  indicated  by  the  sizes 
of  the  dots.  To  use  these  maps  it  must  be  remembered 
that  as  you  face  the  south  greater  right  ascensions  are  on 
your  left  hand,  less  on  your  right.  The  right  ascensions 
of  the  stars  immediately  to  the  south  between  6  and  7  P.M. 


are  : 


For  January  1,  1  hour; 
"  February  1,  3  " 
"  March  1,  5  " 
"  April  1,  7  " 
"  May  1,  9  " 
"  June  1,  11  " 


For  July  1,  13  hours; 

"  August       1,  15      " 

"  September  1,  17      " 

"  October      1,  19      «• 

"  November  1,  21      " 

"  December  1,  23      " 


By  remembering  these  precepts,  and  by  tracing  the 
alignments  of  the  brighter  stars,  the  map  can  be  used  to 
identify  every  constellation  marked  on  it. 


INDEX. 


THIS  index  is  intended  to  point  out  the  subjects  treated  in  the 
work,  and  further,  to  give  references  to  the  pages  where  technical 
terms  are  denned  or  explained. 


Aberration-constant,    value     of, 
178. 

Aberration  of  light,  174. 

Achromatic  telescope  described, 
63. 

ADAMS'S  work  on  perturbations 
of  Uranus,  256. 

AIRY'S  determination  of  the  den- 
sity of  the  earth,  148. 

Algol  (variable  star),  296. 

Altitude  of  a  star  defined,  18. 

Angles,  3. 

Annular  eclipses  of  the  sun,  135. 

Apparent  place  of  a  star,  16. 

Apparent  time,  45. 

ARISTARCHUS  determines  the  so- 
lar parallax,  165. 

Asteroids  defined,  191. 

Asteroids,    number    of,    225    in 
1882,  238. 

Astronomical     instruments     (in 
general),  60. 

Astronomy  (defined),  1. 

Atmosphere  of  the  moon,  231. 

Atmospheres  of  the  planets.    See 
Mercury,  Venus,  etc. 

Axis  of  the  earth  defined,  21. 
Azimuth  defined,  19. 


BESSEL'S  parallax  of  61  Cygni 

(1837),  315. 
Binary  stars,  302. 
BODE'S  law  stated,  193. 
BOND'S  discovery  of  the  dusky 

ring  of  Saturn,  1850,  250. 
BOUVARD  on  Uranus,  256. 
BRADLEY  discovers  aberration  in 

1729,  176. 
BUNSEN,  339. 

Calendars,  how  formed,  182. 
CASSINI  discovers  four  satellites 

of  Saturn  (1684-1671),  852. 
Catalogues  of  stars,  general  ac- 
count, 79. 

Celestial  sphere,  14. 
Centre  of  gravity  of  the  solar 

system,  194. 
Chronology,  180. 
Chronometers,  68. 
CLARKE'S  elements  of  the  earth, 

152. 

Clocks,  68. 
Clusters  of  stars,  308. 
Comets,  general  account,  274. 
Comets'  orbits,  277. 
Comets'    tails,    repulsive    force, 

277. 


348 


INDEX. 


Comets,  their  physical  constitu- 
tion, 276. 

Comets,  their  spectra,  277. 

Conjunction  (of  a  planet  with 
the  sun)  defined,  97. 

Constellations,  288,  342. 

Construction  of  the  heavens,  317. 

Co-ordinates  of  a  star,  19,  37. 

COPERNICUS,  103. 

Correction  of  a  clock  defined,  69. 

Cosmogony,  322. 

Corona,  its  spectrum,  216. 

Day,  how  subdivided  into  hours, 
etc.,  187. 

Days,  mean  solar  and  solar,  46. 

Declination  of  a  star  defined,  41. 

Distance  of  the  fixed  stars,  314. 

Distribution  of  the  stars,  318. 

Diurnal  motion,  21,  22. 

Dominical  letter,  186. 

DONATI'S  comet  (1858),  281. 

Double  (and  multiple)  stars,  301. 

Earth,  general  account  of,  142. 

Earth's  density,  142. 

Earth's  dimensions,  151. 

Earth's  mass,  142. 

Eclipses  of  the  moon,  131. 

Eclipses  of  sun  and  moon,  129. 

Eclipses  of  the  sun,  explanation, 
132. 

Eclipses  of  the  sun,  physical 
phenomena,  212. 

Eclipses,  their  recurrence,  136. 

Ecliptic  defined,  84. 

Elements  of  the  orbits  of  the  ma- 
jor planets,  198. 

Elongation  (of  a  planet)  defined, 
97. 

ENCKE'S  comet,  283. 

ENCKE'S  value  of  the  solar  paral- 
lax, 8".  578,  166. 


Epicycles,  their  theory,  102. 
Equation  of  time,  188. 
Equator  (celestial)  defined,  21. 
Equatorial  stars,  344. 
Equatorial  telescope,  74. 
Equinoxes,  87. 
Eye-pieces  of  telescopes,  62. 
FABRITIUS  observes  solar   spots 

(1611),  207. 

Figure  of  the  earth,  148. 
FRAUENHOFER'S       Experiments 

with    the   Prism,    335;   Lines, 

335,  337. 

Future  of  the  solar  system,  332. 
Galaxy,  or  milky  way,  319. 
GALILEO    observes    solar    spots 

(1611),  207. 
GALILEO'S  discovery  of  satellites 

of  Jupiter  (1610),  240. 
GALLE  observes  Neptune  (1846), 

259. 
Gases,  spectra  of  incandescent, 

338;  in  meteoric  stones,  341. 
Geodetic  surveys,  150. 
Golden  number,  184. 
Gravitation  extends  to  stars,  303. 
Gravitation  resides  in  each  par- 
ticle of  matter,  119. 
Gravitation,  terrestrial,  146. 
Greek  alphabet,  11. 
Gregorian  calendar,  185. 
HALLEY  predicts  the  return  of  a 

comet  (1682),  279. 
JELALi/s  discovery  of  satellites  of 

Mars,  235. 

HANSEN'S  value  of  the  solar  par- 
allax, 8".  92,  166. 
HERSCHEL  (W.)    discovers   two 

satellites  of  Saturn  (1789),  252. 
HERSCHEL  (W.)  discovers    two 

satellites  of  Uranus  (1787),  254. 


INDEX. 


849 


HERSCHEL  (W.)  discovers  Uranus 
(1781),  253. 

HERSCHEL'S  catalogues  of  nebu- 
lae, 305. 

HERSCHEL'S  star-gauges,  318. 

HERSCHEL  (W.)  states  that  the 
solar  system  is  in  motion  (1783), 
312. 

HERSCHEL'S  (W.)  views  on  the 
nature  of  nebulae,  305. 

HIPPARCHUS  discovers  preces- 
sion, 153. 

HOOKE'S  drawings  of  Mars 
(1666),  234. 

HORIZON  (celestial— sensible)  of 
an  observer  defined,  17,  20. 

Hour-angle  of  a  star  defined,  39. 

HUGGINS'  determination  of  mo- 
tion of  stars  in  line  of  sight, 
310. 

HUGGINS  first  observes  the  spec- 
tra of  nebulae  (1864).  309. 

HUYGHENS  discovers  a  satellite 
of  Saturn  (1655),  252. 

HUYGHENS  discovers  laws  of 
central  forces,  116. 

HUYGHENS'  explanation  of  the 
appearances  of  Saturn's  rings 
(1655),  248. 

Inferior  planets  defined,  99. 

lutramercurial  planets,  226. 

JANSSEN  first  observes  solar  pro- 
minences in  daylight,  213. 

Julian  year,  184. 

Jupiter,  general  account,  240;  ro- 
tation-time, 242;  satellites,  243. 

KANT'S  nebular  hypothesis,  323. 

KEPLER'S  laws  enunciated,  109. 

KIRCHHOFF,  339. 

LAPLACE'S  nebular  hypothesis, 
323. 


LAPLACE'S  investigation  of  the 
constitution  of  Saturn's  rings, 
252. 

LAPLACE'S  relations  between  the 
mean  motions  of  Jupiter's  satel- 
lites, 243. 

LASSELL  discovers  Neptune's  sat- 
ellite (1847),  260. 

LASSELL  discovers  two  satellites 
of  Uranus  (1847),  254. 

Latitude  (geocentric  —  geogra- 
phic) of  a  place  on  the  earth  de- 
fined, 8,  31,  41,  152. 

Latitude  of  a  point  on  the  earth 
is  measured  by  the  elevation  of 
the  pole,  31. 

Latitudes  and  longitudes  (celes- 
tial) defined,  95. 

Latitudes  (terrestrial),  how  deter- 
mined, 53. 

LE  VERRIER  computes  the  orbit 
of  metoric  shower,  271. 

LE  VERRIER'S  researches  on  the 
theory  of  Mercury,  226. 

LE  VERRIER'S  work  on  perturba- 
tions of  Uranus,  257. 

Light-gathering  power  of  an  ob- 
ject-glass, 63. 

Light-ratio  (of  stars)  is  about  2.5, 
295. 

Line  of  collimation  of  a  telescope, 
71. 

Local  time,  47. 

LOCKYER'S  discovery  of  a  spec- 
troscopic  method,  216. 

Longitude  of  a  place,  9,  10. 

Longitude  of  a  place  on  the 
earth  (how  determined),  50,  52. 

Longitudes  (celestial)  defined, 
95 

Lucid  stars  defined,  289. 


350 


INDEX. 


Lunar  phases,   nodes,   etc.     See 
Moon's  phases,  nodes,  etc. 

Magnifying  power    of    an  eye- 
piece, 65. 

Major  planets  defined,  191. 

Mars,  physical  description,  233. 

Mars,  rotation,  234. 

Mars's  satellites    discovered    by 
HALL  (1877),  235. 

MASKKLYNE  determines  the  den- 
sity of  the  earth,  145. 

Mass  of  the  sun  in  relation   to 
masses  of  planets,  167. 

Mean  solar  time  defined,  45. 

Mercury's  atmosphere,  244. 

Mercury,  its  apparent   motions, 
221. 

Meridian  (celestial)  defined,  27. 

Meridian  circle,  72. 

Meridians  (terrestrial)  defiued,27, 

Melon ic  cycle,  183. 

Meteoric  showers,  269. 

Meteoric  stones,  gases  in,  341. 

Meteors    and    comets,   their  re- 
lation, 271. 

Meteors,  their  cause,  265. 

Milky  Way,  289. 

Milky  Way,  its  general  shape  ac- 
cording to  HERSCHEL,  319. 

Minor  planets  defined,  191. 

Minor  planets,  general  account, 
237. 

Mira  Ceti  (variable  star),  296. 

Months,  different  kinds,  182. 

Moon,  general  account,  228. 

Moon's  light  <ig1000  of  suns,  232. 

Moon's  phases,  123. 

Moon's  parallax,  161. 

Moon,  spectrum  of  the,  341. 

Moon's  surface,  does  it  change? 
232. 


Motion  of  stars  in  the  line  of 
sight,  310. 

Nadir  of  an  observer  defined,  18. 

Nautical  almanac  described,  79. 

Nebulae  and  clusters  in  general, 
304. 

Nebulae,  their  spectra,  309. 

Nebular  hypothesis  stated,  322. 

Neptune,  discovery  of,  by  LE 
VEUKIER  and  ADAMS  (1846), 
256. 

Neptune,  general  account,  256. 

Neptune's  satellite,  260. 

New  stars,  298. 

NEWTON  (I.)  Laws  of  Force,  115; 
calculates  orbit  of  comet  of 
1680,  280;  Spectrum  Analysis 
experiments,  334. 

Objectives,  or  object-glasses,  60. 

Obliquity  of  the  ecliptic,  91. 

Occultations  of  stars  by  the  moon 
(or  planets),  140. 

OLBERS'S  hypothesis  of  the  ori- 
gin of  asteroids,  239. 

OLBERS  predicts  the  return  of  a 
meteoric  shower,  269. 

Old  style  (in  dates),  185. 

Opposition  (of  a  planet  to  the 
sun)  defined,  85. 

Parallax  (annual)  defined,  58. 

Parallax  (horizontal)  defined,  56. 

Parallax  (in  general)  defined,  50. 

Parallax  of  the  sun,  161. 

Parallax  of  the  stars,  general  ac- 
count, 314. 

Parallel  sphere  defined,  28. 

Penumbra  of  the  earth's  or  moon's 
shadow,  131. 

Photosphere  of  the  sun,  201. 

PIAZZI  discovers  the  first  asteroid 
(1801),  237. 


INDEX. 


351 


Planets,  their  relative  size  exhib- 
ited, 191. 

Planetary  nebulae  denned,  306. 

Planets;  seven  bodies  so  called 
by  the  ancients,  81. 

Planets,  their  apparent  and  real 
motions,  96. 

Planets,  their  physical  constitu- 
tion, 261. 

Poles  of  the  celestial  sphere  de- 
fined, 21. 

POUILLET'S  measures  of  solar  ra- 
diation, 205. 

Practical  astronomy  (defined),  78. 
Precession  of  the  equinoxes,  153. 

Prime  vertical  of  an  observer  de- 
fined, 19. 

Prism,  The,  333. 

Problem  of  three  bodies,  119. 

Proper  motions  of  stars.  312. 

Proper  motion  of  the  sun,  312. 

PTOLEMY  determines  the  solar 
parallax,  166. 

Radiant  point  of  meteors,  270. 

Radius  vector,  107. 

Reflecting  telescopes,  66. 

Refracting  telescopes,  60. 

Refraction  of  light  in  the  atmos- 
phere, 169. 

Resisting  medium  in  space,  281. 

Reticle  of  a  transit  instrument, 
71. 

Retrogradations  of  the  planets 
explained,  100. 

Right  ascension  of  a  star  defined, 
40. 

Right  ascensions  of  stars,  how 
determined  by  observation,  72. 

Right  sphere  defined,  29. 

ROEMER  discovers  that  light 
moves  progressively,  175. 


ROSSE'S  measure  of  the  moon's 

heat,  232. 
Saros  (the),  140. 
Saturn,  general  account,  246. 
Saturn's  rings,  248. 
Saturn's  satellites,  252. 
Seasons  (the),  92. 
SECCHI,    on    solar    temperature, 

206. 

Semidiameters  (apparent)  of  ce- 
lestial objects,  59. 
Sextant,  76. 

Sidereal  time  explained,  43. 
Sidereal  year,  153. 
Signs  of  the  Zodiac,  90. 
Solar  corona,  etc.    See  Sun, 
Solar  corona,  extent  of,  213. 
Solar  cycle,  185. 
Solar  heat,  its  amount,  204. 
Solar  motion  in  space,  312. 
Solar  parallax, history  of  attempts 

to  determine  it,  165. 
Solar    parallax    probably  about 

8" -81,  168. 

Solar  prominences  gaseous,  213. 
Solar  system,  description,  190. 
Solar  system,  its  future,  220. 
Solar  temperature.  206. 
Solstices,  94. 
Spectroscope,  The,  335. 
Spectroscopic  observations,  340. 
Spectrum  Analysis,  333. 
Spectrum  of  Solar  prominences, 
214;  Solar  corona,  216;  Lunar, 
341;  Mercury  and  Venus,  262; 
Nebulae    and     Clusters,    309; 
fixed  Stars,  309;  as  indicating 
motions  of  stars,  310;   Solids 
and  Gases,  336;  Solar,  336. 
Star-clusters,  308. 


352 


INDEX. 


Star-gauges  of  HERSCHEL,  318. 
Stars — had  special  names  3000 
B.C.,  291 ;  magnitudes,  290,  345; 
various  magnitudes,  how  dis- 
tributed, 294;  parallax  and  dis- 
tance, 314;  about  2000  seen  by 
the  naked  eye,  291;  proper 
motions,  312;  spectra,  310, 
340;  map  of  the  northern,  343; 
map  of  the  equatorial,  844. 
STRUVE'S  (W.)  parallax  of  alpha 

Lyras  (1838),  315. 
Summer  solstice,  88. 
Sun's  apparent  path,  86. 
Sun's  Atmosphere,  339,  340. 
Sun's  constitution,  217. 
*H3un'8  (the)  existence   cannot  be 

indefinitely  long,  220,  325. 
Sun's  mass  over  700  times  that 

of  the  planets,  194. 
Sun,  physical  description,  200. 
Sun's  proper  motion,  312. 
Sun's      rotation-time    about    25 

days,  200. 
Sun,  Speclroscopic  observations 

of  the,  340. 

Sun-spots  and  faculae,  200,  206. 
Sun-spots  are  confined  to  certain 

parts  of  the  disk,  208. 
Sun-spots,  their  nature,  209,  340. 
Sun-spots,  their  periodicity,  211. 
Superior  planets  (defined),  99. 
SWEDENBORG'S  nebular  hypothe- 
sis, 323. 
SWIFT'S  supposed   discovery  of 

Vulcan,  226. 

Symbols  used  in  astronomy,  11. 
Telescopes,  66,  337. 
Telescopes  (reflecting),  66. 


Telescopes  (refracting),  60. 
TEMPEL'S  comet,  its  relation  to 

November  meteors,  272. 
Temporary  stars,  298. 
Tides,  126. 
Total  solar  eclipses,  description 

of,  212. 

Transit  instrument,  70. 
Transits  of  Mercury  and  Venus 

225. 

Transits  of  Venus,  163. 
Triaofulation,  150. 
Tropical  year,  154. 
Twilight,  172. 
TYCHO  BRAHE  observes  new  star 

of  1572,  299. 
Universal  gravitation  discovered 

by  NEWTON,  121. 
Universal     gravitation     treated, 

113. 

Uranus,  general  account,  253. 
Variable    and    temporary    stars. 

general  account,  296. 
Variable  stars,  theories  of,  299. 
Velocity  of  light,  179. 
Venus's  atmosphere,  224. 
Venus,  its  apparent  motions,  221. 
Vernal  equinox,  87. 
Vulcan,  226. 
WATSON'S  supposed  discovery  ol 

Vulcan,  226. 

Weight  of  a  body  defined,  143. 
WILSON'S   theory    of    sun-spots, 

210. 

Winter  solstice,  89. 
Years,  different  kinds,  183. 
Zeniih  defined,  17. 
Zodiac,  90. 
Zodiacal  light  272. 


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